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Atoms, Molecules and Nuclei Q.63  The de-Broglie wavelength of a particle having a momentum of 2×10-28kg m/s is

          (a.63) 3.3×10-5m  (b.63) 6.6×10-6m  (c.63) 3.3×10-6m  (d.63) 1.65×10-6m

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Q.64  A proton and an α particle are accelectrated through the same potential difference. The

ratio of the de-Broglie wavelength of the proton to the de-Broglie wavelength of the α

particle will be

          (a.64)          (b.64) (c.64)   (d.64)

Composition And Size Of Nucleus

Nucleus: - positively charged and high density centre.

99.9% mass of the atom.

Protons(+ve) + neutrons(neutral)= nucleons

number of protons = atomic number (Z).

number of protons & neutrons = mass number(A).

nucleus symbolically expressed as

For example, gold: - and Uranium: - .

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Radius of nucleus

R = R0 where R0 is linear constant = 1.2 × 10-15 m.

volume of nucleus α A.

Density of nucleus is constant = 2.3 × 1017 1kg/m3,

radius of carbon nuclei is

Radius of uranium nuclei is

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Isotopes, isotones and isobars

Isotopes: - The nuclei have same number of protons

but different number of neutrons. E.g. deuterium

tritium are the isotopes of hydrogen. gold has 32

isotopes. Isotopes have identical chemical behavior

and are placed in the same location in the periodic

table.

Isobars: - The nuclei have same mass number (A). For

example, the nuclei are isobars.

Isotones:- The nuclei having same number of neutrons

(A – Z) but different atomic numbers Z. For example

are isotones.

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Mass-Energy relation

Einstein proved that mass is a form of energy.

E = mcE = mc 22

Energy of electron.

Ee = mec2= (9.1 × 10-31) × (3 ×108)2 joule

= 0.511 × 106 eV = 0.511 MeV

Similarly, the energies of proton and neutron are

Ep = 941.1 MeV and En = 942.2 MeV

There is one more unit used to express nuclear

masses. It is Unified atomic mass unit. It is (1/12)th

of the mass of neutral carbon atom in its lowest

energy state. Its symbol is ‘u;

1u = 1.66054 × 10-27 = 931 MeV/C2

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OR Energy equivalent of mass 1 u is = 931 MeV

Mass Defect

It is observed that the mass of a nucleus is smaller

than the sum of the masses of constituent nucleons in

the Free State. The difference between the actual

mass of the nucleus and the sum of masses of

constituent nucleons is called mass defect.

Let M – be the measured mass of nucleus.

A – be the mass number (mass of

nucleons in free state)

Z - atomic number (number of protons)

Mp - mass of hydrogen atom (i.e. proton)

Ma - Mass of free neutron

(A – Z) - number of neutrons.

The mass defect △m = [Zmp = (A – Z)mn] – M

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Nuclear Binding Energy

Nucleons (protons and neutrons) are bound together in

a nucleus with very strong attractive force. Energy

must be supplied to the nucleus to separate its

constituent nucleons. It is observed that mass of the

nucleus is always less than the sum of the masses of

its constituent nucleons. The difference in mass is

being used as energy that holds nucleons together.

The amount of energy required to separate all the

nucleons from the nucleus is called binding energy of

the nucleus.

The B.E. of nucleus is very high. For example, it is 2.22

MeV for deuteron nucleus, whereas B.E. for an atom,

say hydrogen atom in its ground state is 13.6 eV. That

is, B.E. of nucleus is about 10,00,000 times larger than

B.E. of atom.

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The B. E. of nucleus can be expressed in terms of

mass defect. B.E. = △m × c2 joule

Where △m is mass defect and c is speed of light.

But △m = [Zmp + (A – Z)mn] – M

∴ B. E. of nucleus = [Zmp + (A – Z)mn – M]c2 joule

The B.E. per nucleon =

This is average energy per nucleon to separate a

nucleon from the nucleus.

B.E. Curve

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The B.E. curve is an indicator of nuclear stability. The

higher the B.E. per nucleon, the greater is the stability

From B.E curve we can infer as follows:

i. The B.E. per nucleon is practically constant and

is independent of mass number for nuclei,

30 < A < 170.

ii. It is maximum 8.75 MeV, for A = 56 and is 7.6

MeV, for A = 238.

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iii. It is low for both light nuclei (A < 30) and heavy

nuclei (A > 170). This means that the nucleons of

atoms are loosely bound with nucleus.

iv. When heavy nucleus (A = 240) breaks into lighter

nuclei (A = 120), B.E. increases i.e. nucleons get

more tightly bound.

v. When very light nuclei A < 10, join to form a heavier

nucleus, B.E. increases, i.e. nucleons get more

tightly bound.In both the cases, there is release of

energy because, the new nuclei formed have less

mass and are more stable.

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Radioactivity

Becquerel

Heavy elements like uranium, radium having A > 82

are unstable and emit highly penetrating radiations.

The substances which emit these radiations are known

as radioactive substances.

The phenomenon of spontaneous emission of

radiations from radioactive substance is known as

radioactivity.

Radioactivity is property of atom and nuclei, hence is

unaffected by chemical or physical changes. 11

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Radioactivity is nuclear phenomenon in which an

unstable nucleus undergoes decay. It is called

radioactive decay.

There are three types of decay –

i. -decay - .

ii. -decay - electrons or positrons.

iii. -decay - high energy photons.

Properties of –particles12

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1. +ve. It is helium atom with both electrons removed.

Mass:- 6.64×10-27kg & charge +3.2×10-19 coulomb.

2. It is deflected by electric and magnetic field.

3. The speed of emission of -particles depend upon

the nature of radioactive element. It varies from

(1/10)th to (1/100)th of the speed of light.

4. Affect photographic plate, produce fluorescence.

5. They ionize gas when passed through gas.

6. Range:- through air:- 2.7cm to 8.62cm for thorium.

7. They are scattered when incident on mica,

aluminium and gold foil.

8. When an -particle is emitted by an atom, its

atomic number decreases by 2 and mass number

decreases by 4.

e.g.

Properties of -particles

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1. -rays are fast moving electrons

2. Their speed ranges from 1% to 99% of the speed of

light.

3. Being charged particles they are deflected by

electric and magnetic field.

4. They can ionize gas but its ionization power is

of that of -particles.

5. They are more penetrating than -particles.

6. Their range in air depends on their speed. A -

particle of 0.5 MeV has a range of 1 m in air.

7. When -particle is radiated, the atomic number

increases by 1 and mass number does not change

e.g.

Properties of -rays

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1. -rays are not particles but they are

electromagnetic waves (photons) of very short

wavelength. Photons originating from the nucleus

are called -rays.

2. They are neutral in charge and not affected by

electric and magnetic field.

3. They affect photographic plate and produce

fluorescence.

4. They have very low ionization power about

of that of σ a-particles.

5. They have high penetration power and can pas

through 25cm thick iron plates.

6. They are diffracted by crystals.

Radioactive Decay law

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The spontaneous breaking of nucleus is known as

radioactive disintegration.

They decay law

The number of nuclei undergoing the decay per unit

time is proportional to the number of unchanged nuclei

present at that instant.

Let N be the number of nuclei present at any instant t,

dN be the number of nuclei that disintegrated in short

interval of time dt. Then according to decay law:

Where λ is known as decay constant or disintegration

constant.

From equation (1)

Integrating both sides

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loge N = –λt + c

where c is constant of integration whose value

depends on initial conditions.

At t = 0; N = N0 (the number of original nuclei)

∴ loge N0 = 0 + c

Substitution the value in above expression

loge N = – λt + loge N0

loge N – loge N0 = – λt

Or N = N0 e-λt ...(2)

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This expression shows that number of nuclei of

given radioactive substance decreases exponentially

with time.

Decay constant

From equation (1) we have

The decay constant is defined as ratio of the

amount of substance disintegrated per unit time to

amount of substance present at that time.

We have N = N0e-t

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Let us define ‘t’ as t =

N = N0e-1

N =

N =

N = 0.37 N0

The decay constant , which is equal to , can be

defined as reciprocal of time duration (t) in which the

substance decays to 37% its original quality.

Half life period (T)

Half life period (T) of radioactive substance is

defined as the time in which the half substance is

disintegrated.19

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We have N = N0e-t

at t = T; N =

∴ = N0e-T

or = e-T

or et = 2

T = loge 2 = 0.693

∴ T =

Using this expression, we can determine the half

life of radioactive substance if its decay constant is

known.

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Nuclear fission

Discovered by:- German scientists Otto Hahn and

Strassman(1939)

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Nuclear fusion

When two lighter nuclei are fused to form a heavier

nucleus, the process is called nuclear fusion.

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