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EUROPEAN SCHOOLS

1998-D-45 Orig.: FR Version: EN

Physics Syllabus for 6th and 7th years

(Approved by the Board of Governors on 28 and 29 April in K~benhavn))

Will enter into application

in year 6 in September 1998 in year 7 in September 1999

European Schools May, 1997.

Physics Programme, years 6 and 7.

Preamble Page 1

I. Introduction.

The 4 period option course is the last turn of the spiral of physics education in the European schools, which revisits many of the topics introduced in the 4th and 5th year, bringing more depth to them and adding links to other areas of the discipline.

It is a final programme of physics study for a significant number of pupils; and for some, a preparation to follow scientific courses at a higher level, at university or elsewhere.

11. Aims.

Since the course is rooted in the 4th and 5th year work it shares the aims spelt out in considerable detail in the preamble to that course, to which reference should be made.

To these must be added the requirement, imposed by the principle above, that pupils should reach a level of factual knowledge and intellectual skill which will enable them to begin a university science or engineering course with as good a chance of success as a pupil who has followed a 6thnth year physics course in a member state.

In addition. the notion of a scientific model takes a very explicit place for the first time at this level. Pupils should understand the barrier which stands between model and reality, and should come to appreciate the power and the limitations of models such as the wave model of light or the various models of the Hydrogen atom.

Ill. Selection and teaching.

I. Target population.

(a). Future professionals.

The course will be of direct relevance for pupils who wish to follow courses which are academic and scientific in character, for example physics itself, engineering, architecture or mathematics; but many pupils choosing other courses would also be well supported by having studied physics at school level, either for vocational reasons or as part of a general education.

(b). The educated citizen.

A study of physics at this level can provide an opportunity for pupils who do not necessarily see themselves as having a future directly in science to develop, in a practical fashion, an important part of their

European Schools May. 1997.


Preamble Page2

general education and culture. The society in which we live is technically very sophisticated, and many decisions must be made to which scientific knowledge at an intermediate level can contribute.

2. Access qualifications.

Pupils wishing to follow the 4 period option in the 6th and 7th year should have shown good evidence in 5th year that they are interested in the subject and are capable of achieving good marks at that level without undue strain. Like most 6th year options, a faster pace will be expected, and more intellectual demands will be made, than was the case in years 4 and 5. Pupils who had difficulty achieving pass marks there should not consider this option.

It is also desirable that candidates should have a certain facility in mathematics. This does not necessarily imply that they must follow the 5 period maths course; however, pupils in the first category described above should certainly do so. Others who see this option as part of their general education and who are good at mathematics may wish to do the 3 period mathematics course in order to have time to spare to invest elsewhere; but those who have a difficult time with maths will not find the physics course accessible.

3. Teaching approach.

There is no such thing as a non-practical science course; for the essence of scientific activity is to observe, relate observations one to the other, draw conclusions, make predictions and test these. Therefore the phenomena underpinning the cognitive knowledge of physics embodied in the course must as far as possible be observed in the laboratory or classroom, and it is highly desirable that pupils should themselves perform as much practical manipulation as the limited course time allows.

In addition to this, pupils should learn to use traditional means (reference books and private study) to help themselves, as well as the methods which modem computing makes available to science. These include:

- computerized gathering and logging of data -computerized data processing - simulation - use, where appropriate, of multimedia reference material and of resources offered by the Internet.



Preamble Page3

Pupils should also understand clearly the limitations of computer-based methods, so that they do not think (for example) of simulations as experiments.

IV. Material and assessment.

The material covered in the course is summarized as follows.

6th year course:

Section M. Mechanics. 2 and 3-dimensional kinematics and dynamics of point-like masses. Vector formulations. Conservation of energy and momentum. Uniform circular motion. Simple hannonic motion.

Section F. Electric and magnetic fields. Uniform and radial electric field, electrical potential and potential energy. Capacitance. · The uniform magnetic field, the solenoid. The Hall Effect. Electromagnetic induction.

Optional Study. One of the following topics should be chosen: Special Relativity. Mechanics of Rigid Bodies. Alternating Current. Thermodynamics.

7th year course:

Section F. Field Physics. Energy in inver~e square and unifonn fields. Movement of particles in fields.

Section W. Waves. Sinusoidal waves. Equiuion.anp examples of a progressive wave. Refraction, reflection, diffraction, interference. Stationary waves, eigenvalues. The Doppler Effect.



Preamble Page4

Section D. The dual character of matter and radiation. Corpuscular behaviour of light. The photoelecuic effect. Momentum of light. Diffraction of particles. De Broglie waves.

Section A. Atomic physics. The nuclear atom. Spectral series. Eigenvalues for the Hydrogen atom's energy.

Section N. Nuclear Physics. Elementary particles. The nucleus. Mass-energy equivalence. Mass defect and binding energy; binding energy per nucleon. Fission and fusion. Reactors. Exponential radioactive decay: half-life. Radioactive series.

Pupils ' success in the course will be assessed in accordance with the rules governing the general evaluation at the end of the 6th and 7th years. including the rules of the European Baccalaureate examination. Some notes on assessment are attached as an appendix to the programme, which should be read alongside the appendix for the programmes of the 4th and 5th years where more detail is available.

Questions for the written baccalaureate will be based on the programme of the 7th year, although they may call on knowledge acquired earlier. ·Knowledge of material covered only in the optional sections of the 6th year course will not be assumed.

European Schools May, 1997. I


Appendix Page 1

... Guidelines for the writing of examination questions.

Questions for assessment in years 6 and 7 of the physics course, and in particular questions for the Baccalaureate written and part examinations. should observe the guidelines set out in the appendix to the programme for the 4th and 5th years q.v., with appropriate adjustments for the level. In this connection it is appropriate to bear in mind that the candidates for these evaluations have selected an optional course, as compared to those in years 4 and 5 for whom physics is obligatory. Some of these guidelines are reproduced below. with additions particularly applicable to the examining process in years 6 and 7.

l.

..,

3.

4.

5.

6.

Questions should have a good balance of elements; not too much which is cheap recall, and not too much which demands very original thinking. They should in the main examine the general understanding of physical principles, and not memory or the ability to substitute into formulae .

The balance described above should be such that a pupil of average ability in the subject, who has worked well, can comfortably get a mark of 6, and could get 7 or even 7.5 with sufficient application.

Notwithstanding the above, an attempt should be made to provide some material in each question which is accessible to students of lower ability (cheap recall at the average level); but this should not account for a large proportion of the total marks. A similar stipulation should apply to harder material designed to enable good students to show what they can do.

Questions should not be so long as to intimidate the pupil with the task of reading them thoroughly and understanding the material. This is particularly noteworthy for 6th and 7th year pupils, a significant number of whom will be working in a foreign language because of the difficulty of opening options in smaller language sections.

It is desirable as far as possible to devise questions which draw (at least in some of their parts) on a range of topics within the programme rather than being confined narrowly to one topic only; it is a better test of ability, and avoids "political" or selective revision for papers which often involve a choice of a relatively small number of questions.

Whilst questions should remain focussed on the principles in the programme itself. this does not exclude setting questions which require candidates to apply these principles to other situations which are not specifically mentioned in the second column of the text, provided that the these applications are fairly direct and that an entire question is not based solely upon them.

r The European Schools

Harmonized Programme for Physics, year 6. Page 1 May, 1997.

PROGRAMME IIEAD/N(;

Sectitm M. Mecllatlics.

1\11 Kinem:tlil"s. 1\11.1 \h:lnr

represenl:al inn.

1\11.2 Uniform and uniformly accelerated motion.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Savoir-Faire".

In this programme, formulae cited In the text are derived, and pupils should, if asked, be capable of deriving them, whereas

Formulae and definitions given In boxes should be 1 known by pupils, and may be quoted without proof.

Bold Type is used in this text to denote vector quantities.

Displ:acement from a specified origin. velocity. and :acceler:ttion all behave in accordance with a vector model. Revision of definitions and relationships in basic kinematics. see programme of years 4 and 5. sections K2. K3. introducing the ,·eclor nature of these quantities.

~----------------------------~ Velocity Symbol: v Unit: ms·1

Definition: v = As/M

Instantaneous velocity= Urn (As/M)= dsldt tJ.t ..... o

Acceleration Symbol: a Unit: ms-2

Definition: a= Urn (Av/M) = dv/dt {)1 ..... 0

Average velocity Symbol: <V> or v Definition: <V> = Total vector displacement/Total time

Equations of uniformly accelerated motion: v = v0 +at s = v0t + at2!2

AVENUES OF APPROACH

The European Schools

Harmonized Programme for Physics, year 6. Page 2 May, 1997 .

...

MI.J

Ml.4

PROGRAMME HEADING

Combination of ,·eJocities. Projectile mo,·emenl.

Time: 16 periods (M I)

Ml Dynamics. Ml.l Basics.

M2.2 The elastic force.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sm·oir-Faire".

Addition and resolution of uniform velocities in two dimensions .

Addition of two perpendicular velocities, one of which is uniform and the other uniformly accelerated. l11is situation obtains when a projectile moves without air resistance under gravity. and results in a parabolic path. Pupils should be able to relate later velocities. positions and directions to initial conditions. time of flight etc.

Revision of basic dynamics. see 4th and 5th year programmes sections M4.1 to M4.5. introducing and underlining the vector nature of force. Addition and resolution of forces in rwo dimensions. The work should be limited to a consideration of point or point-like

bodies.

Fres = r.F F,85 = 0 <=> v = constant

Fres = ma

FAB=-FsA

In addition to the forces alread studied, the elastic or spring force should be introduced) The extension of a stretched spring is

proportional to its tension.

Elastic Force.

F =- klls where k is known as the spring constant.

Connected systems such as lifiJS. rowed and towing vehicles ere should be treated, as should movement under non-parallel

systems of forces. e.g. on the ihclined plane. J.

L-------------~----------------

A\'ENUES OF APPROACH

Practical investigations: air table, siToboscope .... . Trigonometrical or vectorial rreatment. Drift velocity: tides currents . air- and ground speeds

Experiment~ in rrains.lifts. rockers ere. Bodies falling in water.


Harmonized Programme for Physics, year 6. Page 3 May. 1997.

PROGRAMME /lEADING

M2.3 Oissipath·e force.

M2.4 Universal gravitation.

M2.5 Variation of g. Time: 10 periods (Ml)

M3. Conservation laws. M3.1 Energy

MATERIAL AND IDEAS TO BE COVERED: definitions. units,formulae and "Savoir-Faire". AVENUES OF APPROACH

parachute A qualitative discussion of the effect of dissipative forces (solid and fluid friction) should be included. Final speed of falling bodies

Two spherically symmetrical bodies of mass M and m whose centres of mass are separated by a distanced attract mutually, with Cavendish 's balance. a force proportional to their masses and inversely proportional to the square of their separation.

Gravitational Force.

where G is the universal gravitational constant.

At a distance r from a planet of mass M the value of the gravitational intensity is g = GMfrZ; if 8o is the value at the surface (radius R) then glg0 = R2frZ. The treatment extends only to point masses or masses with spherical symmetry. The inverse square field. e.g. of a planet, for vertical displacements which are trivial compared with radius, approximates to a uniform field .

Macroscopic interactions and reactions result in no overall change of total energy. though there may be exchange or conversion from one form of energy to another. llte work done by the resultant force acting on any body is equal to the change in its kinetic energy.

W= F·t\s

W = t\Ek= t\(mv2!2)

Near the surface of the Earth the gravitational force may be considered to be constant. thus gravitational potential energy is proportional to height above a given datum. The work done by an elastic force is the product of average force and displacement.



PROGRAMME HEADING

M3.2 Momentum.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu[ae and "Savoir-Faire".

W9 = AE9 = F·As = mg·h

We1= <F>·As

For an initially unstretched spring We/ = A Eel= '12F·As = '12 k As2

In the absence of friction, the sum of a body's kinetic energy and its potential energies associated with such forces as the gravitational and the elastic force is constant (sometimes known as the mechanical energy of the body).

The vectorial aspects of the calculation of work should be emphasized. and cases where the force and displacement are nonparallel should be treated. Pupils should be able to cope with energy conservation and transfer in situations involving exchange of energy under all the forms met in the programmes of years 4 and 5.

A steady force F, acting for a time At on a body modifies its velocity.

FresM = mAv (constant mass)

AVENUES OF APPROACH

Energy exchange in a weight bobbing on a spring Rollercoasters

lt may be possible with a fast 11 fnllnws th:•l if the resull:ml force is um thl· ljllantity mv is :1 cunsavcd qu;mtity. lltis is the ntmncnfurn of I he hody. Till' left l!rnup. whl·rc the hand sille of this ClJUilliun is I he lmpul._c of :1 fon.:c. thermodyn:unics option has nnl [Note: Can• is m•ctlrtl ill tlrc trlttl.\'latimr of ''lmpul.n··· (= Kraft.,·tll.\·.,·) ullll "Mom<'llfum" (= lmpulsJ ;,,,am/from Gaman and heen chosen. to look at gas .mm'' othrr lcmguuge.r.] 11ressure here.

Momentum Symbol p Unit kg ms·1

p = mv

Experimental study of explosions and collisions. "Newton's cradle".



PROGRAMME~

!lEADING

M3.3 Collisions. Time: 16 periods (MJ)

M4 Uniform circular motion.

M4.1 Basics.


For a system of two or more bodies to which all forces are internal. the law of action and reaction implies that the sum of momenta is constant. These laws may be wriuen in tenns of momentum in a more fundamental way.

Fres = dpldt in general

= ma (constant mass)

r.mnvn =constant (for a closed system)

No quantitative work on systems of variable mass is required.

A collision subsequent to which bodies adhere and thus move together is called a perfectly inelastic collision. A collision

AVENUES OF APPROACH

Recoil of artillery: landing gear: rocket engine: se;~r bells: water jets.

However. able groups might look at variable mass syslems e.g. rockets in flight

which conserves kinetic energy is called a perfectly elastic collision. Both should be studied, in one and in two dimensions. Gramophone turntables: llte law of conservation of momentum, being based on the law of action and reaction, applies to both categories. Kinetic energy rotation and revolution of lhe

is dissipated as heat in an inelastic collision. Earth.

The movement of a point moving around another (fixed) point may conveniently be described by the angle. in radians. swept oul in a given time, and by the radius. The angle described per second is the angular velocity. It is not essential at this level to insis t on the vectorial character of angle or of angular velocity.

, The European Schools

Harmonized Programme for Physics, year 6. Page 6 May, 1997,

PROGRAMME HEADING MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sa1·oir-Faire".

Angle

Symbol: o Unit: radian rad

Definition: 9 = dlr (d = arc length, r = radius)

Angular velocity

Symbol: c•> Unit: rad s·1 or s·1

Definition: eo= 69/6t

ro = vir

T = 2rt/ro = 1/f

M4.2 Centripetal force. A resultant force is required to cause such a body to perform uniform circular motion. since such a body cannot be in equilibrium. This force must be directed towards the centre of the circle, and therefore causes an acceleration towards the

centre. The acceleration required to produce a given circular trajectory depends on the values of radius and angular speed required. The force producing this acceleration is called the centripetal force.

a cent = v2fr = ro2r

F cent = mv2/r = m ro2 r

AVENUES OF APPROACH

Experimental verification Centrifuge, spin dryer. Coriolis force. Planetllry movement. Weight at poles and equator Conical Pendula etc

For completeness. Kepler's laws might be noted. but it will be difficult to tie them in with the rest of the course unless I he

~4.3 Satellite motion.

"rotating bodies" option is

The movement of a satellite under the gravitational force can result in a circular orbit, whose period is given by T1 = 41C2r·'IGM. taken. where M is the mass of the central body. Thus the mass of the satellite is irrelevant.

IM4.4 Frames of reference. An observer in a rotating frame of reference observes an "inertial force" known as the centrifugal force. Time: 8 periods ( M4} Teachers may use methods based on this or on centripetal force to resolve problems on circular motion. as they choose,



PROGRAMME HEADING

1\15 Simple Harmonic motion.

MS.I Basics.

M5.2 Energy exchange between oscillators.

Time: 10 periods (MS)

Section F. Electric and mtlgnetic fields.

F. I The electric field. Fl.l Basics.

MATERIAL AND IDEAS TO BE COVERED: definitions, units, formulae and "Sm·oir-Faire". AVENUES OF APPROACH

A body is said to perfonn simple harmonic motion if a "restoring .. force exists which is always directed towards a fixed point. and is proportional in magnitude to the body's distance from this point. An equivalent definition is that the body's displacement Refer to 3.1 above . from a fixed point varies sinusoidally with time. Pupils should be able to demonstrate the equivalence of these statements.

Examples of simple harmonic or approximately simple harmonic motion include the bob of the simple pendulum and the movement of a mass under the elastic force. with or without the action of gravity.

If the sum of kinetic and potential energies is constant the amplitude of the motion will be independent of time, and the motion i~ said to be undamped. If this is not the case. then the amplitude decreases with time giving damped simple harmonic motion (usually due to frictional forces of some kind).

Simple Harmonic Motion

Definition:

Velocity:

Acceleration:

Energy:

F =- kx or x = A sin rot (k>O)

v = Aro cos rot

a = -Aro2 sin rot = - o:ilx

where ro = 21tf = 21tl T

E = ~mA2ro2

An oscillator can communicate its movement to another which is linked to it in some way. If the two oscillators have the same period, the response of the second can readily result in small stimuli producing significant movement. This phenomenon is known as resonance. Examples and applications should be explored but a quantitative investigation is not required.

An electric field is said to exist in a region of space where a body experiences a force proportional to its electric charge. The direction of the electric field is in the direction of the force observed on a positive test charge. The intensity of the field is the force observed per unit test charge.

The similarity between gravitational and electric fields may be exploited



... PROGRAMME

HEADING

Fl.l llniform electric field.


Electric field intensity Symbol: E

Definition: E = F/0

Unit: NC·1, Vm·1

A uniform field is said to exist when the magnitude and direction of E are constant within a region. A good approximation to a uniform electric field is observed between two parallel conducting plates with a potential difference between them.

Fl.3 Electrical potential The definition of electric field implies that a charge moving parallel to the direction of an electric field will gain or lose energy. and potential This energy is known as electrical potential energy. The definitions of potential difference (commonly called voltage). work energy. and electric intensity lead to simple formulae for the value of the work done in the course of such movement.

Work done in an electric field W=OAU

= F·As = E·OAs if the field is uniform.

·n,e elcctric:tl potenti:tl :at ;a point is the electrical potentiill energy per unit ch;arge sihmted at that point. As is nornml when dealing with potenti:tl energy. the point al which electric:al P. E. is t:tkenas zero is arhitrary. ('nmmon conventions are that

a) test charges at a very large distance from any other OOdy, or b) test charges situated on a conductor connected to the earth

are taken as possessing zero potential energy. and that therefore the points at which such charges are situated may be taken to be

at zero potential. Thus the basic equation shown above may be rewritten in terms of potentials rather than potential differences. lt is necessary to distinguish work done by the field from work done by an external agent moving a test charge against the field direction.

AVENUES OF APPROACH

Electric field line maps

Equipotentials

A fast group may be able to approach the idea of a calculus formulation of this topic.

Discussion of the sign of WAR



FIA

PROGRAMME HEADING

The radial electric tield.

Tim~: 16 puiods (FI)


Electrical Potential UA = EA/0

whence the work done to move a charge in an electric field is

WAs= Q(Ue- UAJ

A point charge (or a spherically symmetrical distribution of charge. eg a charged conducting sphere) is surrounded by an electric field whose intensity depends directly on the total charge and inversely on tl1e square of the distance from the point. The intensity of this field also depends on a property of the medium in which the charge is placed. defined as its permittivity.

Intensity due to a point charge. E = 014rttr2

Permittivity The quantity E is the permittivity of the medium in which the experiment is conducted.

Relative Permittivity Symbol: E,. Unit: None

Definition: Er = fiEo

There is an inverse square Jaw of force between two point charges Q1 and Q2 separated by a distance r.

Force between two point charges F =EO= 0,0214ttEr2

AVENUES OF APPROACH

It may be possible to treat the capacitance and potential due to an isolated sphere.

1l1e comparison with gravity may again be exploited.

Coulomb's experiment Practical work with batteries. electrolytic capacitors and resistances.



F.l Fl.l

PHUvRAMMI:. /lEADING

Capacitance. Basics.

f2.2 The parallel plate capacitor.

fl.3 Energy storage.


Any conductor may be charged. and as a consequence change its potential. If a system consists of two conductors which are initially at the same potential, charge may be transferred from one to the other by some outside agent (e.g. a battery or a power supply), causing the p.d. between the plates to increase. This p.d. is found to be proportional to the amount of charge transferred. The ratio is defined as the capacitance of the system. and it depends on the dimension.c; of the conductors and on other parameters of the system.

Capacitance

Definition: C = OIU Unit: farad F = CV·1

Two parallel plates. separated by an insulator, constitute a capacitor of particular interest, whose capacitance is a simple function of the area of the plates, their separation and the permittivity of the insulator separating them.

Capacitance of a parallel plate capacitor Relation: C = rAid

whence E = Cd!A

and hence E may be expressed in Fm-1

Work is done in charging the capacitor, and energy is stored in a charged capacitor as electrical potential energy, which can be recovered on discharge. The stored energy is calculated using the mean value of the voltage during the charging process.

Energy stored in a charged capacitor E = !t2 OU = !t2 CLJ2 = !t2 02/C

AVENUES OF APPROACH

Capacitor Hash, electret and capacitor microphones. smoothing.

Water conrainer analogy

Possible mathematical formulation of the exponential law, if the level of the class permits.



F2.4

F2.5

PRUC,UAMM£ HEADING

Time to charge and discharge a capacitor.

Capacitors in combination.

Tim~: 8 periods (Fl)

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sa~·oir-Faire".

TI1e energy stored in such a system may be compared in many ways with that stored in a stretched spring. see above. The idea of an exponential charging process should be introduced informally. Pupils should be aware that the time to charge a capacitor to a certain proportion of the supply voltage is proportional to capacitance and resistance. and that this allows capacitors to be used as timing devices. A meaningful time constant may be calculated depending only on resistance and capacitance values.

The combined capacitance of parallel capacitors is equal to their sum, whereas in a series circuit, adding more capacitive elements reduces the effective capacitance.

_Parallel Circuit:

c = C1 + C2 + c3 + .......

Series Circuit: 1/C = 11C1 + 1!C2 + 1/C3 + ...... .

Time Constant:

T=RC

F 3. The magnetic field. Formulae associated with electromagnetism are given in "scalar form", i.e. without an attempt to express them

FJ.I Basics.

IF3.l The current element.

rigorously with vectors.

The work from year 5 on the basic magnetic fields due to a current-carrying wire etc. should be revised, again emphasizing vector aspects of the material.

A current element (i.e. an infinitesimally short wire carrying a current) placed in a magnetic field experiences a force, proportional to the current and to the length of the element, which varies with the intensity of the magnetic field. This permits a measure of the intensity or magnetic induction of the magnetic field, as the force per unit current per unit length. The sense and orientation of the current element with respect to the magnetic field also indicate the direction of the field.

AVENUES OF APPROACH

A group who are very good at vector mathematics might manage a rigorous treatment.

The Biot-Savart law may be introduced.



PROGRAM rH!: /I f::\l>/.f\1(; MATF.RIAL AND lnEAS TO BE COVf:RF.D: definitions, units,fnrmu/ac and "Sm·oir-Fairc".

Magnetic Induction or Magnetic Flux Density.

Symbol B Unit: tesla T = NA1m-1

F = 8 i t-.L sinG

F3.3 The unirorm magnetic field. The solenoid.

In the middle of a long solenoid. the magnetic induction is unifom1 and depends on the current and on the number of turns per metre of length. lt also depends on a property of the medium inside the solenoid. known as its permeability.

F3.4

Magnetic Induction due to a solenoid. 8 = 11ni = !J.Ni I I

For a vacuum (or approximately for air)

11 = llo = 47t x 10-7 TA1m-1

Permeability , The quantity 1-1 is called the permeability of the medium in which the experiment is conducted.

Relative Permeability Symbol: llr Unit: None

Definition: llr = J.LIIlo

Moving charges in a Free charged particles moving perpendicular to a magnetic field also constitute a current and experience the force described in magnetic: field. 3.2 above. Hence charge carriers traversing a conductor placed normal to a magnetic field experience a deflection giving rise to

the maintenance of a p.d. across the conductor. known as an emr. 'The direction of this p.d. permits the sign of the majority charge carrier to be determined; in conductors. the majority charge carriers are found to be negatively charged. A practical rule to determine the direction of the emf should be taught.

AVENUES OF APPROACH

Experimental work.

Hall voltage is the product of B carrier velocity and breadth of the conductor. In doped semiconductors and in fluids the carriers may be of either or both signs.

1t is not appropriate to insist on the technical definitions of flux and induction. which would require the weber 's definition to come before that of the tesla. A capacity to work wit11 these quantities is sufficient.



PROGRAMME HEADING

F3.5 Electromagnetic induction.


Moving charge in a magnetic field.

F= 8qvsin9

The magnetic induction may profitably be pictured as consisting of lines of magnetic flux(') whose density is equal to the magnetic induction. If a wire is moved perpendicular to a magnetic field there will be an emf induced across it. This emf is also present when the ftux linking a closed circuit varies, and these two processes may be thought of as equivalent. The phenomenon is known as electromagnetic induction. Conservation of energy implies that any resulting current is in such a direction as to oppose the change responsible for producing it. The action of the dynamo uses this phenomenon.

Magnetic Flux.

Symbol ' Unit: weber Wb = Tm2 = Vs

8 ='/A where 8 l. A

Induced emf U =- A4l/M =-M81M = 8vl

[Note: Care is needed in translations of the term em/. which seems not tn be used in modern textbooks in several languages.]

A varying current in a solenoid will cause a varying magnetic field along its axis, which will also link any adjacent closed circuit. Thus an emf will be induced in the solenoid itself proportional to the rate of change of current (self-induction) and in the adjacent but electrically unconnected circuit (mutual induction). The action of the transfonner relies on mutual induction.

AVENUES OF APPROACH

If the a.c. option is not chosen, there may still be time with an able group to look at power transmission.



PROGRAMME HEADING MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Savoir-Faire". AVENUES OF APPROACH

Tim~: 16 periods (FJ).

Sution 0. OptioMitopics. On~ ofth~se topics should

b~ claos~nfor stmly.

01. The mechanics of rotating rigid bodies.

Self and Mutual Inductance.

Symbol L,M Unit henry H = VsA-1 = Wb A-1

In one circuit, U c:x d'ldt = - Ldildt

Between two circuits. U c:x ~ldt = - Mdildt

Conditions of the equilibrium of a rigid body: the Principle of Moments. Rotational Kinematics; angular velocity ro. angular acceleration c:x

ro = roo + c:xt e = Cllo 1 + * c:xr1

e = *<roo + Cll)f etc.

Rotational kinetic energy and the Moment of Inertia.

The moments of inertia of simple bodies: point. hoop. disc. rod. sphere. The parallel axis theorem.

Rotation;• I tlymunics and torque T.

T= lc:x T llt = t1l ro

oi = roi + 2a0



PROGRAMME HEADING

02. A.C. circuits. 02.1. Production of an

A.C.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Savoir-Faire".

Angular Momentum and its conservation.

L =fro

(Note: A .rimple treatmellt. restricted to 2 dime11sio11s. mdy i~:11orr thr ••ector nature of torque and treat it as a positil'e or IU'/:Util'e quallfity. accordilll( to it.r docklt·i.w• or amidod:ll'isc scnsr. Thi.t dors not of coursr exclude the full u.tr ofT= r x F and oftlw I'C'UIIr nmure of cm~:ular quumitirs ll'itlr afu.w group.]

When a coiltums in a homogeneous magnetic field. a sinusoidal altt>mating current is produced.

U(t) = U0 sin rot (I) = lrif = 2nff

02.2. Effective values of The effective value (r.m.s. value) of an alternating voltage or current is the value of the D.C. equivalent which would dissipate current and voltage. the same average power. Thus for sinusoidal wavefom1s

023. Phase angle difference between U and I. Impedance. Frequency dependence.

J~JJ = /0 J..J2 U#J = Uoi..J2

The impedance Z of an electric component or circuit is defined as Z = UcJio = U~1JI~ff· For a pure resistance Z = R. but for reactive components (inductors or capacitors) the impedance is frequency dependent. and a difference of phase angle Acjl is observable between U and I.

M =- rtll (V lags 011 /)

Acjl = rr./2 (V leads on I)

TI1ese phenomena may be studied with an oscilloscope.

AVENUES OF APPROACH



... PROGRAMMt:

HEADIN!i MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Savoir-Faire".

02.4. The lr-C-R series Experimental study of a series circuit consisting of resistance. capacitor and inductor shows that at low and high frequencies . circuil. one of the reactive terms CZc or ZL) dominates. causing a net phase angle difference which is correspondingly positive or

negative.

~2.5. Resonance. The oscillator.

03. Kinetic Theory and Thermodynamics.

03.1 Basics. Absolute Zero.

03.2 Properties of temperature.

03.3 The zeroth law of thermodynamics.

03.4 Model of the ideal gas and its real approximation. Absolute zero.

z = ..J/ R: + (Z, - Z1y I

At a particular frequency Z becomes purely resistive and the phase angle difference is zero. This resonance phenomenon is characterized by a sharply peaked minimum of impedance. The resonant frequency is given by

ro= ltV(LC)

In an ideal situation where R = 0, we would obtain Z = 0 at resonance. Consequently self-sustained oscillations would occur if the driving generator were to be replaced by a short circuit.

Revision of 5th year work. Heat (internal) energy of molecules, temperature. The definite amount of internal energy possessed by a body implies that energy cannot be removed without limit. and suggests that there may be a limit also to how low temperature can be.

Temperature difference is the factor which causes energy to move from one body to another.

If two bodies are at the same temperature as a third. they are at the same temperature as each other. They do not necessarily possess the same amount of internal energy.

Pressure of an ideal gas: simple derivation from elementary ideas of pressure and momentum of the expression for the pressure of such a gas.

P = (Nm <cZ>) 13, where Pis the gas pressure. N the number of molecules and m the molecular mass.

AVENUES OF APPROACH



~3.5

O.HI

~H.7

04. 104.1

PROGRAMME HEADING

Reversibility. Organiz:tlion and entropy.

The second I:IW ur lhermodyn:~micc;

Gas engines; trading heat for work. The first law or thermodynamics.

Special Relativity. The principle of relativity.

MATERIAL AND IDEAS TO BE COVERED: definitions, tmits,formu/ae and "Sm•oir-Faire".

This relation implies that PV is proportional to ,m.: . which may be considered to be proportional to intemal energy and thus to temperature in a simple model of constant specific heal capacity. Such a model implies an absolute zero of remperalure which may be calculaled as- 273°C approximately. In a real gas al low pressure with a h1rge mean free path this is found to he the case to a good approximation.

PVIT has a constant mlue for a ~il'l'll ma.u of !(OS.

Some changes in nature (burning. levelling. mixing ..... ) obviously cannot be reversed without providing significant amounts of energy. All real mechanical operations involve dissipative forces of some sort, and waste some energy as heat to the environment. Apparenlly reversible changes (pendulum) are only approximately so. All natural changes show a tendency to change from highly organized to states to stales which are less so. The lJUantity enlropy measures the amount of disorder in a system. Entropy inue;1scs in n;alural. "irn:vnsihlt~ .. proccsst's.

Wmk Gill he co mpletely convertcJ to heal bul hc;1l cannol he cnml•letely convertcJ to work. Thus the wn.-JJ is gaining ht~at energy all the ti me. and without some organizing agt~nl can never lose ir again. This is lhe second law of thermodynamics and is e4uivalen1 to slilling !hilt heal t:nergy cannot hy itself " run uphill"" fwm :1 body allow tcmpcmrm·t: loa hoJy al high ternperaturt: (this would result in increased entropy).

Internal energy of a gas can be partly traded for work. A sink for waste heal is required as well as a source of high grade heal. in accordance with experience and in agreement with the st:cond law. lt is a theoretical impossibility to invent a car engine which does not heat the world up. both through friction and from some of the energy provided by the fuel.

Motion observed within and from outside moving systems: lhe idea of an inertial frame.

104.2 The velocity of light. Einstein assumed that the speed of light is constant in all inertial systems. Experiment supports this assumption. TI1e velocity of

light is a universal natural constant.

AVENUES OF APPROACH



PROGRAMME HEADING

0 ... 2.1 Timl' dilalinn.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sat•oir-Faire" .

llu:! const:ml:y of the speed of ltght has consequenct's fur the qu:ullities of length. lime and mass in different inertial systems.

To an observer moving with a velocity ,. relative to an inl'rtial frame. events in th<1t inertial frame occur more slowly than they would to an observer who is stationary in it. The ohserved time interval t\1 is related to the so-called proper time interval 610 .

04.2.2 Length contraction. Likewise. observed distances in a direction parallel to the relative velocity I' are shortened by a factor k (the FitzGerald-Lorentz contraction)

04.2.3 Mass-energy equivalence.

'rrimt 12 periods (0)

1l1e mass of a body depends on its velocity relative to the observer:

m = m0 I (I - (vlcjZJ'~r

Generally a mass m is equivalent to an amount of energy E. which allows the classical laws of conservation of energy and of

mass to be assimilated into one single law

E=mc2

The increase of mass /!m of a moving body corresponds to the amount of kinetic energy Ert which it possesses:

AVENUES OF APPROACH

...... --



PRO(,RAMMt; HEADING MATERIAL AND IDEAS TO BE COVERED: definitions, wzits,formulae and "Savoir-Faire".

7th year programme. Formulae given In frames may be quoted without proof In answers to Baccalaureate questions. Candidates for the Baccalaureate may be required to derive other formulae. Timings are suggested, not obligatory.

~ection F. Fi~ld Physics. To separate two bodies of masses m1 and m2 from separation ra to separation rh requires an amount of work given by

F 1. Energy in the inverse square field. W = Gmlmz (lira -1/r").

Fl.l The gravitational

field.

Fl.2 The electric field.

Revision of work from year 6, sections M2.4, M2.5. M4.3. Conventionally gravitational potential energy is taken as zero at infinite separation. This implies that gravitational potential energies are negative, since the gravitational force is attractive.

Gravitational Potential Energy Ep =- Gm1m21r

in a radial gravitational field

The escape velocity for a body at radius r from a planet of mass M (for example) is consequently given by V map~ = (2GM/rf y,

The mechanics of circular movement imply that the kinetic energy of an orbiting body is Ek = Gm1m212r. implying a total energy for a satellite of- Gm1mz12r.

By exact analogy. the total energy of a light charged particle in circular orbit around a stationary massive charged particle follows.

Electrical Potential Energy

Ep =- o,02!8rtEor in a radial electric field

AVENUES OF APPROACH

Gravitational potential may be introduced.

Calculations of the mass of the sun and of planets: orbital speed. ll1e journey to the moon.



PROGRAMME HEADING

FI.J The electron ,·olt.

F 2. Energy in the unirorm field.


I For sman particles, of atom1c or subatomiC d1mensJons. '' 1s convemenl (especially 1f they are charged) to measure tlletr energy in a smaller unit than joules. The energy of a particle whose charge is equal to that of the electron. which has been accelerated from rest by "p.d. of I v. is defined as I electron volt (le V).

Electron Volt Unit: eV

Definition:

the energy equivalent to that of

an electron accelerated from rest by a p.d. of 1 V

F2.1 The uniform Revision of basic work from years 4 and 5. and from 6th year. M3.1. gra,·itational field.

F2.2 The uniform electric Revision of work from year 6, Fl.l - F.l.3. field.

F2.J The magnetic field. Since the force on a moving charged particle in a magnetic field is perpendicular to its velocity vector, there is no work done and hence no modification of the particle's kinetic energy.

F3. Movement of a particle in a field.

F3.1 Uniform Revision of work from year 6. M 1.4 gravitational fields.

F.l.2 llniform electric As in the unifonn gravitational field, the genemlmuvementof a charged particle in a uniform electric lielt.l is parabolic.

AVENUES OF API'ROACH

F.l . .l fields. llnifonn nmgnctic fields.

"Jlte equalions governing rhe movemenl of a char~cd partidc in a magnclic field imply thal rhe gencmlmuvemcnl is helical: helix degenemtes to 11 circle if lhe velociry 11nd intensity vectors are perpendicular ;~nd toil slraight line if lhey ;~re parallel. ·nu: rat.lius or the circuh1r movement is given by r = n11·1Bq. [Nole: llrrr ox rl\·rwhl'fl' a ri~omu.\· l't'Uortrratmrllf is

tllllleu.uory, but pupil.v should be ah/e to u.vr a prut·tinJI rule to clrdua the .rrll.fl' of the fin-er].

the Analogies with ftee fall and wilh b:~llistic prohlems. The linear :~cceleratur.



PRU(,f<AMME /IF.ADIN(;

t-'.t4 Applic:ahons. Timr: 32 ptriotiJ (FJ

~ection W. U'm·es. Wl. Basics. Wl.l Delinitions.

Sinusoidal waves.

W 1.2 Equation of a progressh·e wave.

MATERIAL AND IDEAS TO BE COVERED: definitions, wzits,formu/ae and "Savoir-Faire".

1 A magnetiC fieJO may be used to distmgu1sh p;ut1cles accoromg to ffieu masses. as 111 the mass spectrometer. Elecrnc fields can he used to speed particles up. as in the electron gun. Electric or magnetic fields can be used to deflect them as in the oscilloscope or the television tube. Electric and magnetic fields in combination can be used to select particles by velocity or to accelerate them. as in a cyclotron. Other simple uses of fields in parallel and perpendicular combination are not excluded.

A system of oscillators. arranged so that the energy from one may be communicated by some mechanism to its neighbours. can give rise to the propagation of a progressive wave. Thus energy is transported without the bulk movement of any mass.

Wave!~ may be transverse or longitudinal in nature. according ro whether the di .~turbance is respectively perpendicular or p;uallelto the direction of energy travel.

If the disturb<mce y of a given oscillator is given by y =A sin wt (see year 6). then it is termed a harmonic or sinusoidal oscillator. :md O>t is known as its phase angle. 1l1e disturbance of a neighbouring oscilh•tor will be identical in amplitude. assuming no energy loss. but different in ph:1se angle. Its disturbance will therefore bey'= A sin( cot- t1l/>). where A~ is the difference of phase angle between them. The phase <mgle ch:mges linearly with displacement in the direction of movement of the wave, for a given value of time. [Note: the term "Phase" does not IJa,·e tire same implicatiom in all languages. In the European Schools it is appropriate. to a\•oid possible contradictions and problems of translation. to refer to the phase angle at a point rather than the phase at a poilll .

lfor example.]

In a progressive wave.

the phase angle of a given oscillator will change by 21t in time 2n/ro. This is the period T of the wave. the phase angle of an oscillator is modified by 2rt for two oscillators separated by distance A.. This is the

wavelength. for two oscillators separated in distance by Ax and in time by At. the difference in phase angle is

The equation or a progressive wave is y =A sin(2ntl T - 2ru:IA.)

A wave may thus be defined as doubly periodic (in space and in time).

AVENUES OF APPROACH

Other accelerators. e.g. the synchrotron. The electron microscope. magnetic lenses, Millikan.

Demonstrations with coupled pendula etc.



PROGRAM M/.:: IlEA DIN<; MATERIAL AND IDEAS TO RE COt'ERED: dcfinitirms, units,formu/ae and "Sm·oir-Faire".

TI1e speed of prop;~gation of •• wave is Ar/tlt =AI T =[A. :md expresses the speed of movement of a wavecrl"'st (or other point o given phase angle).

AVENUES OF APPROACH

\\'1.3 lluyghens' print:iple. A progressive wave may be considered to propagate by the generation of secondary wavelets along its wavefront.

\VIA Examplt~.

Wl. Beha,·iour. :Wl.l General

Wl.l Refraction.

General note: The cmrcrpt of a wm•e a/lm,·s Uflflaremly twy di.uimilar flhenomena to he tlescriiJed hy very similar wa1·e models. This uspecr should he emplra.fi::ed in rlris secrion. hy underlining tire simi/ariry n/tfre heh01·iour f/or example) ofsnuncl and radio. rather tlran rhrir contrasts. Sound or Acoustic waves may be propagated in solids. liquids and gases. In air, the speed of propagation is about 340 ms·l at Velocity or waves on a wire: room temperature. but is temperature dependent. Sound waves are longitudinal in gases. Transverse waves may be propagated c2 = F/Jl where~·= m!/ (the on wires with a velocity dependent on tension and linear density. linear density of the wire)

Velocity or sound waves: Electromagnetic waves have a very large range of frequencies and can be used to carry information (radio), to see by (light). and ·'T h r · 1 b 1 1 for medical purposes (:lf.-rays) according to the frequency used. TI1ey are transverse, may travel through a vacuum, and do so independently of their frequency with a velocity c which is one of the fundamental constants of physics. lt is not necessary to examine in depth why they are called electromagnetic and how they are propagated, at this level.

Refraction, reHection, diffraction, interference and the Doppler effect may be observed in all waves.

A train of waves which change their propagation velocity. usually because of some modification of the medium in which they travel. will also modify their wavelength in proportion (but not their frequency). At oblique incidence this leads to a change in direction. If the angles with the nonnal to the interface between the media are ex and ~. and the velocities are et and ~ in the

two media respectively, then sinalsin(J = c/c2•

Refractive Index of a medium

Symbol: n

Definition: n = c/c' where

c = wave speed in a vacuum

c' = wave speed in the medium

c ex ~ w ere ts t 1e a so u e temperature.

The phenomena should be demonstrated with as diverse a range of waves as possible (light, sound. ripple tank, microwaves. ultrasound .... )



PROGRAMME HEADING

W l.j HeflccCmn.

W2.4 Diffraction.

W2.5 Interference. 12.5.1 Basics.

2.5.2 ( :uhcn~un·.

2.!U Slatiouary w:nes.


A tram of waves rellecl from a surface wiiJ1 an "equal angles law. If file surface from which the rellect1011 takes place IS of a medium in which the wave's velocity would be lessened. the reflection is accompanied by a phase angle change of n.

A plane wave passing through an aperture will "spread out" to an extent which depends on the wavelength and on the aperture size. This effect is significant in proportion to A/d. where d is the width of the aperture. Similar behaviour occurs when a wave encounters an obstacle.

AVENUES OF APPROACH

Two waves which coincide at a point in space and time will give a resultant disturbance which is the sum of the individual Beats disturbances. This is the principle of superposition. If this results in an increase in amplitude (reinforcement) there is constructive interference. If the amplitude is reduced. there is destructive interference. For superposition of identical waves. the resultant wave will have an amplitude between zero and double that of the two interfering waves. If the sources of the two waves are situated at points A and B. and are in phase. then at any point P. interference is constructive if the path difference is a whole numher of wavelengths. and destructive if it is an odd number of half wavelengths.

I Stable interference helmviour will be observable only hctwcen two waves which have a constant phase relationship lotmt• anotht~r. Such w;1ves ;1rc s;1id lo be coherent. Sourrcs of sud1 waves arc coherent sources.

Path difference.

Symbol: o Unit: m

Definition: o =IPA- PB I at a point P

where A and Bare the positions of two coherent sources.

These result from the interference of identical waves travelling in opposite directions. Nodes and Antinodes result at points of destructive and constructive interference, which are al fixed positions in space. The waves must be from coherent sources: but they may in general be of any frequency. Points at which interference is destructive (called displacement nodes) are separated by half a wavelength. and between each pair of nodes there is a displacement antinode at which interference is constructive.

, .., The European Schools


""'

~.5.4

PROGRAMME HEADING

Bounded media; fundamenhlls :and O\'ertones.

~.5.5 Double source interference.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sm•oir-Faire".

1 [Note: in French the term ~statlcinaiy wal-e~ seems only to he used/or wa1·es which exist 1111 a huu11ded medium. whmone wave is produced hy reflection of an11tlrer .. fee helm,·. Care must l1e taken tll ai'Oid pmh/ems of tram/at ion when preparinJ? Bacca/aur('ate que stim1s.]

A most important case of stationary waves arises when the medium in which the waves propagate is bounded. The only strong stationary waves which can exist are those which match the physical conditions forced at the boundary. Only certain well defined values of frequency can be supported by the system with any significant amplitude. The lowest frequency possible is known as the fundamental: the other frequencies are known as overtones. and their frequencies are simply related to the fundamental. In the fonnulae which follow. n denotes the overtone number. and A.o the wavelength of the fundamental. [Note: the use of the terms "01•ertone" and "harmonic" and their equi1•alents 1•arie s between fang uage s. Great care must tlu•refore he exercised in the setting and tram/at ion of Baccalaureate questions if ambiguity and comradiction are to he avoided. The term "First Harmonic" does not, for example. ha1·e the same meaning in French as it does in EnglisiJ.]

On a string or in an open pipe; In a pipe closed at one end:

A.,. = Aol(n+l) = 21/(n+l) (both ends displacement nodes or both antinodes) A

11 = A.0 1(211+1) = 4/1(2n+ I) (one end a displacement node. one an antinode)

If two coherent sources of waves which are in phase are situated at points A and B which are a distance d apart. a stationary wave will exist along AB (see above): but elsewhere (for points which are not on AB) a system of strong progressive waves may be observed which is symmetrical about the mediator of AB.

For observers at a large distance from AB compared to its length d. the path difference o at an angle x from the mediator of AB

will be o = d sin x. Thus waves of high amplitude arrive because of constructive interference at points where

sin ek = kA.Id. (k is known as the order of the maximum).

Waves of low amplitude arrive because of destructive interference at points where

sine= (2k-l )A./2d

_..j

AVENUES OF APPROACH

Resonance tube experiments: Melde. Kundt.... Organ pipes. and other wind and string instruments.

The single slit diffraction pattern. and its modulation of the double slit pattern, may be treated if the level of the group permits. ......

, ~



"' PROGRAMME HEADING

p.s.6 The diffraction

grating;

W2.6 The Doppler Effect. 'Tim~: 34 p~riods (W)

~~ction D. Th~ dual charact~r of matt~r and radiation.

D.l General.

b~. Corpuscular behaviour of lighL The photoelectric effect.

~

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Savoir-Faire". AVENUES OF APPROACH

I If m addthon lo lhe abOve coridllJOn, lhe angle 9 1s small. and 1f D 1s lhe d1s1ance of rhe observer from AB . !hen

sin 9k .. 9k .. tan {\ = x1JD = k)Jd for a maximum of inrensily.

where Xt is lhe dislance of lhe k1h maximum from lhe symmelry axis. whence il follo ws thallhe maxima of intensity are equally IRefraclomelers. the Michelson spaced wilh separalion DA/d. lnlerferometer. Lloyd. Fresnel..

' llte diffraction grating allows maxima of higher intensily lobe observed al the same angles and pos ilions. and also narrows lh( maxima making them easier to locate. A detailed explanalion of these differences from the double slit case is not required.

When a source of waves S. of frequency f0• and an observer 0 are in relative motion parallel to OS. the observed frequency f of A capable group might treat the the waves will be given by f= c'{).', where c' and ).; are lhe observed velocity and wavelength of lhe wave. Tite observed "moving source" and "moving frequency is therefore affected if the source and lhe observer are approaching or receding from one another. observer" cases for sound.

Observed frequency change - source and observer approaching one another .

M!f = vie (for V<<C)

where vis the speed of approach, c is the wave speed in the medium (if any).

It is usual to consider electrons and other particles as behaving like small objects having mass, and radiation such as light as wave motions, for reasons justified by their behaviour studied above. However. in lhe case of certain aspects of lheir behaviour a reversal of these models is required.

Electrons are emitted from an illuminated pure metal surface in a manner which cannot be satisfaclorily explained by considering light as a wave. There is no emission at all for light which is below what the wave theory would call a certain frequency, known as the threshold frequency. Above this frequency, electrons are emitted immediately. wilh a maximum kinetic energy which varies linearly wilh lhe "frequency" of the light, and an abundance dependenl upon its intensity. The value of this threshold frequency varies with lhe nature of the metal concerned.

Discharge of the electroscope on exposure to radiation.

r ~



"" PROGRAMME HEADING MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Savoir-Faire".

llus behaVIOUr IS perfectly accounted for. quan111at1vely anJ CJllilhtatJVely. by assun1ing light to be propagate<J oy COrpuscles Or photons whose energy varies directly with classical frequency. A given metal has a threshold of energy below which no emission of electrons takes place. This quantity is the work function of the metal.

jo2.2 Measurement of I Abundance and maximum ke of emitted electrons may be measured using a photocell with suitable power supplies and Planck's constant. measuring inslruments. Pupils should be familiar with this experiment, and with its use to measure Planck's constant.

lif= W0 + KE = W0 + ~ m1•1 = W0 + eV-''"1'. and W0 = lif0

D2.3 Momentum of lighl. I A beam of light (or a stream of photons) may be shown to possess momentum which increases with decreasing wavelength.

!D.J Wave behaviour of particles

0.1.1 Diffraction of ' particl~. 'D.U De Broglie wa~·es.

Work Function

Symbol: W0 Unit: joule J

Definition: The minimum energy to extract an electron from a given metal's surface.

Photon energy E=h.f

where h is P/anck's constant.

Photon momentum p = h!A.

Beams of particles with small mass displ<~y wave-like beh;wiour. ;md are able to diffract and interfere like hcmns of light.

The behaviour of such particles may be quantitatively described if they are taken to have a De Broglie wavelength inversely proportional to the momentum. which corresponds with the expression for photon momentum above.

__.j

AVENUES OF APPROACH

Light sail. solar wind. Crooke's radiometer. The Compton Effect.

, ~



"' PROGRAMME /-lEADING

[).\ .. "\ Applications. Time: 14 periods (V)

. '\rc-titm :I. .·1 t11mit· plly.fit'.f.

".I ( ;l'lll'l';llit il'S. Thl' nudl·:u· alum.

t\ .2 Scril"S.

A3 Eigen\·alues for the Hydrogen atom.

1Time: /4 periods (AJ

_..j

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Sm•oir-Faire". AVENUES OF APPROACH

De Broglie wavelength

A.= hlmv= hip

Tilt: \'cry small wavelt:ngths of electrons make tht•rn useful for minoscopy. because they are less affected by diffraction than light. Nonnal diffraction gratings are not tine enough robe useful. but a crystal lattice will cause analogous interference effects. For electron beams reflected from crystal surfaces. successive layers of molecules give rise to multiple reflected beams which can intec'rft•tt• in the usual way. Thus maxima of inll'nsily arc nhsl'IVCd when .rill q,, = 11 A.lld. where d is the laltice spacing .

The cxpc•·imcnls of Rutherford suggeslcd lhat atoms have a very small. massive. positively charged core which is known as lhe

nudcus. ;Kctlllll';lllit:tl hy ckctmm.

Atoms which are excited by eleclrical bombardment. as in a discharge tube. can emit light. Various frequencies are presenl. arranged in a number of differenr series. lltesc photons get their energy from energy loss due to modifications in rhe configuration of the eleclrons. The fact that the frequencies are always the same and are sharply defined implies lhat only

specific energies are possible.

EJtperiments with discharge tubes.

Discussion of the idea of a llte requirement that an orbiting electron's wave must be in phase with itself at all points in the orbit to enable constructive interference to t.ake place implies that an electron can only orbit at radii where nA. = nhlmv = 2rtr. Historically this is called the ~~nodel: al~ models have Bohr condition. madequac1es.

Along with the classical mechanics of electron orbit (section F. I) this allows calculation of the total energy of the hydrogen a ton as E = _ me4J8r.o21r:!

112 llte Franck-Hertz experiment

11

and the frequencies of the emitted photons are fn = me418r.021r·1{/ln: - //m: J where m and n have integral values. This accords suggests electronic energy with observation: different values of n give the different series. levels exist in Mercury atoms.

Fast groups might look at laser

The lines of the Balmer series (given by n = 2) lie in the visible part of the specrrum. The energy lo cause ionization is action.

E = me418E(l!r2

, ~



"' PROGRAMME IIEADIN(; MATERIAL AND IDEAS TO BE COVERED: definitions, units,formulae and "Sm·oir-Faire".

~\'t'L'tion N. Nuclear Pl.y.ut'J. N.l. Elementary particles. I Revision of work from 4th year. section N. N 1.1 Descriptions. ll1e nucleus is formed of the nucleons (proton and the neutron). Pupils should know the basic facts about masses. charges and

composition of the nucleons. the electron(~- particle) ;md the Cl- particle .

,N 1.2 llnits.

!Nt.3 The nucleus.

IN 1.4 Notation.

ll1e atomic mass unit is the "u"; the masses of the neutron and of the proton are approx imately I u.

The unit of atomic mass Symbol: u

Definition: 1u = 1112 mass of a Carbon-12 atom.

Nuclei are made from a number of protons (Z) and a number of neutrons (N). The total mass of the nucleus in u is approximately A= N+Z

A nuclide with N neutrons and Z protons is represented by ~X. The number of electrons for a neutral atom is equal to the atomic number Z. which therefore controls the chemical identity of the atom. Variations are possible in the number of neutrons; this gives different isotopes of the same element. [Note: national textbooks seem to disagree about whether the symbol used above properly denotes an atom or a nucleus;

l{urthermore the terms "nuclide" , and "isotope" arefrequelllly used loosely in textbooks. It is therefore importatlt in the writitl8 of Baccalaureate questions that the conrel.1 or the text of rlre question makes clear what is intended when this notation or terminology is used. in cases where the difference is importallf.]

IN.2 Nuclear reactions IN2.1 Stable and unstable 'Some isotopes are stable. but many more disintegrate spontaneously. These are known as radioisotopes. and are said to be

nuclei. radioactive. When they break up, the great majority emit a- or IJ- particles.

Like the atom. it is possible for a nucleus itself to exist in an excited energy state. and to lose energy of excitation spontaneously.· This energy may be emitted as a high frequency photon. or y- ray.

1N2.2 y-rays.

.... j

AVENUES OF APPROACH

The cloud chamber: photographic emulsions; the Geiger-Muller tube.

, "' The European Schools


\.. ~

PROGRAMME HEADIN(; MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Sm·oir-Faire". A\!ENUES OF APPROACH

IN2 . .1 M:1ss-ent·r~_,.

equh·alence.

IN2.4 Mass defect and binding energy.

N2.5 Binding energy per nucleon.

N2.6 Artificial radioactivity.

N2.7 Fission and fusion.

ll1e theory nf relattvtty allowed the old conservatum laws uf mass anJ energy to be assmulated to one pnncrple, fly descnbmg the equivalence of these two quantities. Thus the total of mass/energy in a system is a conserved quantity.

Mass-energy An amount m of mass is equivalent to

an amount E of energy, where E = mc2.

The mass of a nucleus at rest is found to be less than that of the sum of its parts at rest. The amount by which the mass is reduced is the mass defect- am. Mass/energy is thus released on assembling a nucleus; expressed as energy.this quantity is also known as the binding energy. and it must be restored in order to dismantle the nucleus.

Binding energy E=-amc2

If the mass defect is divided by the number of nucleons in the nucleus, the binding energy gives an idea of how difficult it is to remove one nucleon. and thus of the stability of the nucleus.

Light elements may be made heavier by artificial means. notably by neutron bombardment and absorption. Sometimes this process can cause the stability of a nucleus to be destroyed.

Two nuclei can join together to fonn one heavier nucleus: this is known as fusion. A heavy nucleus can also split into two parts: this is fission. The binding energy per nucleon. as a function of atomic mass. is of such a form that light elements release energy I Stars ..

on fusion and heavy ones on fission. ln particular, fission can provoke chain reactions (e.g. in Uranium-235 and Plutonium). Charge (atomic number) and mass number are conserved in these and other nuclear reactions.

, -., The European Schools


"-PROGRAMME

HEADING

[N2.8 Application of consenation laws.

'N2.9 Reactors.

MATERIAL AND IDEAS TO BE COVERED: definitions, units,formu/ae and "Sm•oir-Faire".

I Pupils should be able to apply ihe law of conservatiOn of hnear momentum to problems involving nuclear interactions and reactions (see 6th year programmes, M3.2) as well as the law of conservation of mass/energy.

No deep understanding of the technology of nuclear reactors is required, but candidates should know the function of moderators, fuel elements and control rods.

_..j

AVENUES OF APPROACH

~:.. Radioacth·e decay. Definitions.

The number of decays per second observed in a sample of a radioisotope is defined as the activity of the sample, and is found to I Decay of Thorium. be proportional to the number of nuclei present. The constant of proportionality is known as the decay constant: this may be interpreted as the probability of one atom of the isotope decaying in unit time.

Activity Symbol: A Unit: becquerel Bq

Definition: The number of decays or events per second

Relation: A=- dN!dt

Decay constant

Symbol: A.

Definition:

Unit: s-1

A. = AIN =- (dN!dt}IN

N3.2 Exponential decay; !The equations above imply an exponential relation between the number of atoms. mass and activity of a radioisotope and time. Half-life.

N = Nae·'JJ m= mae·Al A= Aoe·A.t.

As a consequence the time taken for a given fraction of the radioisotope to decay is characteristic of the isotope. The time for half to decay is known as the half-life and is given by T 'h = In 2/"A..

~3.3 Radioactive series. I The radioactive series associated with an element terminates with a stable isotope. ,Tim~: 14 periods (N)

Units of dose (Gray. Sievert) may be introduced to an able group. as may historic and othe units (Curie, rem, rad).

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