Atoms

Second Year Physics study material

Modern physics possess five important chapters

1. Dual nature of Radiation and Matter

2. Atoms

3. Nuclei

4. Semi conductor electronics

5. Communication systems

Blue print of marks for PUC and CBSE board are as follows

CBSE Board:

For PUC board Karnataka

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Dual nature of

radiation and matter

Atoms and nuclie

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Dual nature of

radiation and

matter

Atoms and nuclie


Modern physics possess five important chapters

1. Dual nature of Radiation and Matter

and CBSE board are as follows

For PUC board Karnataka

1110

3

Atoms and nuclie Electronic devices Communication

systems

Marks weightage

1110

3

Atoms and nuclie Electronic devices Communication

systems

Marks weightage

Second Year Physics study material 2015

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Marks weightage

Marks weightage


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Atoms

1. Write a short note on J.J. Thomson Atomic model?

A) Thomson proposed an atomic model called Plum Pudding model . He assumed

that the positive charge might be distributed continuously throughout a certain small

region and the negatively charged electrons are embedded in it like seeds in a

watermelon.

Failures in J.J. Thomson model :

1. It cannot explain the stability of atom

2. It cannot explain the hydrogen spectrum.

2. Define Spectrum? How many types of Spectrum present?

A) Condensed matter (Like solids, liquids), dense gases emit electromagnetic radiation

continuously which is a mixture of lot of wave lengths or frequencies. This is due to

interaction of Neighborhood atoms and molecules. This results in creating a

Continuous spectrum

Rarefied gases (less dense gases) produces line spectrum like this . It produces lines

only at certain wavelengths. As space between these atoms is very large, radiation

emitted is due to interaction in the atom itself.

Scientists found there is an intimate relationship between structure of atom and the

spectrum of light it emitted. They are like finger prints to human beings.

Balmer identified a simple empirical formula which gives wavelengths of group of

lines emitted by atomic hydrogen.

3. What is Rutherford Atomic model?

1. An atom may be regarded as a sphere of diameter 10-10 m , but whole of the

positive charge and almost the entire mass of atom is concentrated in a small

central core called nucleus having a diameter 10-14 m.

2. The nucleus is surrounded by electrons. In other words the electrons are

spread over the remaining part of atom, leaving plenty of empty space in atom.

3. As the atom is electrically neutral, the total positive charge on the nucleus is

equal to the total negative charge of the electrons in an atom.

4. The electrons are not stationary; the electrons revolve round the nucleus in

circular orbits. The necessary centripetal force provided to them by the

electrostatic force of attraction between the electrons and nucleus.


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4. Explain briefly Alpha Ray scattering experiment?

A) Rutherford performed a series of experiments on the scattering of alpha particles

due to atoms of thin gold foils. (Alpha particles is a helium atom from which two

electrons have been removed)

A beam of alpha particles emitted from

a radioactive source (bismuth) directed

at a thin gold foil. Alpha particles were

collimated into a narrow beam by their

passage through lead metal plate. The

beam was allowed to fall on a thin gold

foil.

They are scattered in different directions

which are detected with alpha particle

detector. The detector consists of

Fluorescent screen coated with zinc

sulphide and a microscope. On striking

the screen , alpha particles produce

scintillations.

They may be viewed through a microscope, and the distribution of number of

scattered particles may be studied as a function of angle of scattering.

Experimental observations :

1. Most of the alpha particles were found to pass through the gold foil with out

being deviated from their paths

2. Some alpha particles were found to be deflected through small angles (< 90

degrees)

3. Some alpha particles were found to be scattered at large angles (> 90 degrees)

4. Some alpha particles ( 1 in 8000) practically retraced their paths or suffered

deflections of nearly 180 degrees.

The graph between number of alpha particles and the angle Scattering is as shown

in figure

Conclusions:

1. As most of alpha particles pass through gold foil

undeflected, so that most of the space in an atom is

empty.

2. Since the fast and heavy alpha particles could be

deflected even through 180 degrees, the whole of the


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positive charge and practically the entire mass of the atom is confined to an

extremely small core called Nucleus.

3. Since 1 in about 8000 particles is deflected through 180 degrees, the size of the

nucleus is about (1/10000) th of the size of atom.

5. Define Impact parameter and Distance of closest Approach?

A) The impact parameter is the perpendicular distance to the closest approach if the

projectile were undeflected. Particles having small impact parameters have large

deflections, while particles having large impact parameter undergoes undeflected.

Distance of closest approach :

An alpha particle which moves straight towards the nucleus in head on direction

reaches the nucleus , that is move close to a distance (ro)

As alpha particle approaches the nucleus, the electrostatic repulsive force due to the

nucleus increases and kinetic energy of alpha particles goes on converting into the

electrostatic potential energy. Now the particle returns back and suffers an angle of

reflection through 180 degrees.

Consider that an alpha particle of mass m possesses initial velocity u , when it is

at largest distance from the nucleus of an atom having an atomic number Z. At the

distance of closest approach, the kinetic energy of alpha particles is completely

converted to potential energy, mathematically

mu2 = (1/4pio) (2e (ze)/ro)

ro = (1/4pio) ((2ze2)) / (1/2 mu2))

from calculations the value is found out to be 4.13 x 10-14 m .

size of the nucleus is of the order 10-14 m.

6. What are the failures of Rutherford Atomic model ?

A) 1. It cannot explain the stability of nucleus . According to classical electromagnetism

a charged particle continuously emits electromagnetic radiation It looses energy

continuously resulting spiral down of electron in to nucleus leads to destruction of

atom.

2. It cannot explain the spectrum of Hydrogen atom.


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7. Write a short note on postulates on Bohrs atomic theory?

A) In order to over come failures in Rutherford atomic model (stability and radiation

spectrum of atoms) , Niels Bohr applied Plancks theory of quantum theory of

radiation to Rutherfords atomic model.

Postulates of Bohrs atomic model :

1. An electron revolves around the nucleus with a definite fixed energy in a fixed

path known as stationary state without gaining or losing the energy. The

stationary state of electron is also known as energy level.

2. Electron can revolve only in those energy levels , in which its angular momentum

is an integral multiple of h/2pi .

L = mvr = nh/2 pi

Where n = 1,2,3.

3. Electron can jump from one stationary orbit to another stationary orbit , if an

energy of difference between two energy levels is supplied

E2 - E1 = h

8. Write a note on Bohrs theory of Hydrogen atom?

A) In a hydrogen atom , an electron having charge -e revolves around the nucleus

having charge +e in a circular orbit of radius r as shown

The electrostatic force of attraction between the nucleus and the electron is given by

Fe =

If m and V are mass and orbital velocity of the electron , then the centripetal force

required by the electron to move in a circular orbit of radius r is given by

Fc =

The electrostatic force of attraction between the electron and the nucleus provides

the necessary centripetal force to the electron

=

= .(1)

According to Bohrs quantization condition, angular momentum of electron

= or =

-----------(2)

Putting the value of v equation in above equation (1)

22 = 1

4


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= 4.

Since n= 1,2,3. , it follows that radius of the stationary orbits are proportional to

n2 .

Bohrs radius : The radius of the inner most orbit (n=1) of an electron in hydrogen

atom is called Bohrs radius.

In the equation (2) substituting the value of r , we get

= (

! )

= !

This equation given velocity of electron in the nth orbit.

From the above equation v

The velocity of an electron is inversely proportional to its principal quantum number.

The total energy of an electron is the sum of potential energy and kinetic energy

Kinetic energy =

Using equation 1 in the above equation , we have , kinetic energy =

The electrostatic potential energy of the electron revolving in a circular orbit of

radius r round the nucleus is given by

Potential energy =

The total energy of electron revolving round the nucleus in the orbit of radius r is

given by

E = Kinetic energy + potential energy

E=

In other words, an electron can have only some definite values of energy , while

revolving in orbits n= 1,2,3 . it is called energy quantization.

Negative sign indicates that an electron and the nucleus form a bound state.

Substituting the respective values in above equation we get


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# = $.% eV

9. Explain briefly Energy levels ?

A) From Bohrs atomic theory we know E 1/n2.

This indicates that the energy gap between two

successive levels decreases as the value of n

increases. At infinity level the total energy of the

atom becomes zero.

The State n =1 is called Ground state and n > 1

states are called Excited states. When electron

goes from lower energy state to higher energy

state , potential energy and hence total energy

increases and kinetic energy decreases. The

energy level diagram of Hydrogen is as shown in

figure.

Total energy of electron is negative implies atomic electron is bound to nucleus.

Energy should be supplied to remove electron from the influence of nucleus. The

minimum energy required to remove an electron from ground state of atom is called

ionization energy. Its value is 13.6 eV.

10. Write a short note on Spectral series of Hydrogen atom?

A) When an electron jumps from higher energy state to a lower energy state , the

difference in energies of two energy levels is emitted as radiation of particular

wavelength. It is known as Spectral line.

Ei = -( 1/4pi0)2 . (2pi2me4/ni2h2)

Ef = -( 1/4pi0)2 . (2pi2me4/nf2h2)

Ef - Ei = h

h = ( 1/4pi0)2 . (2pi2me4/h2)[1/nf2 1/ni2]

If is the wavelength of radiation emitted , then

C = or = C/

1/ = ( 1/4pi0)2 . (2pi2me4/Ch3)[1/nf2 1/ni2]

This equation gives the wavelength of radiation emitted. Here RH is known as Rydberg

constant = ( 1/4pi0)2 . (2pi2me4/Ch3)


1/ = RH [1/nf2 1/n

The various series of spectral lines of

Hydrogen atom are

1. Lyman Series : In this series in which the

spectral lines correspond to transition

electron from some higher energy state to

lower energy state corresponding to n

Where ni = 2,3, 4.

1/ = RH [1/12

These spectral line lies in Ultraviolet region.

2. Balmer Series : In this series in which the

electron from some higher energy state to lower energy state corresponding to n

Where ni = 3, 4,5 .

1/ = RH [1/22

These spectral line lies in Visible region.

3. Paschen Series : In this series in which the spectral lines correspond to transition

of electron from some higher energy state to lower energy state corresponding to n

Where ni = 4,5,6 .

1/ = RH [1/32

These spectral line lies in Infrared region.

4. Brackett Series : In this series in which the spectral lines correspond to transition


Where ni =5,6,7 .

1/ = RH [1/42


5. Pfund Series : In this series in which the spectral lines correspond to transition of


Where ni =6,7,8 .

1/ = RH [1/52


1/ni2]

The various series of spectral lines of

: In this series in which the

spectral lines correspond to transition of

electron from some higher energy state to

lower energy state corresponding to nf =1.

1/ni2]

These spectral line lies in Ultraviolet region.

: In this series in which the spectral lines correspond to transition of


1/ni2]

These spectral line lies in Visible region.

: In this series in which the spectral lines correspond to transition


1/ni2]




1/ni2]




1/ni2]


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spectral lines correspond to transition of

electron from some higher energy state to lower energy state corresponding to nf =2.


of electron from some higher energy state to lower energy state corresponding to nf =3.


of electron from some higher energy state to lower energy state corresponding to nf =4.


electron from some higher energy state to lower energy state corresponding to nf =5.


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11. Write a short note on Debroglie explanation of Bohrs second postulate of

Quantization?

A) Bohrs Second postulate is given as The angular momentum of an electron

nucleus system is quantized

mvr = nh/2pi

Debroglie explained why angular momentum has only those values which are integral

multiple of h/2pi.

According to Debroglie all material particles such as electron in its circular orbit must

be seen as a particle wave. In analogy of waves travelling on string, particles waves too

can lead to standing waves under resonant conditions. A vast number of wavelengths

are produced, but only those wavelengths survive which has nodes at the ends and

form standing wave in the string.

For an electron moving in nth circular orbit of radius rn , the circumference of the

orbit is 2pirn = n where n = 1,2,3

Where is Debroglie wavelength of electron moving in nth orbit.

Now using Debroglie relation for the wavelength 2pirn = n = n h/p

Where P is the momentum of electron. Then P = mV

2pirn = n (h/mv)

This is known as Bohrs Quantization condition

Numerical problems:

Numerical problems dealt with model

1. Distance of closest approach

2. Bohrs model of Hydrogen atom


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Atoms