Summary - Neet

Modern Physics
Rutherford Seattening :
Rutherford seattering experiments helped in understanding structure of atom. Rutherford bombarded a narrow
beam of   particles on a gold foil and observed visible light scintillations on a zinc surplide screen. Rutherford
observed that :
(1) Most of the   particles were either undeflected or deflected through small angles of the order of 1°.
(2) A few   particles were deflected through angles as large as 90° or more.

Bohr Model of Hyrogen atom
Bohr proposed his theory of structure of atom on the basis of following assumptions :
(1) Electrons move in circular orbits about proton under the influence of coulomb force of attraction. These
orbits are stationary states in which electrons do not continuously radiate electromagnetic energy.
(2) The emission or absorption of electron takes place only when there is a transition of electrons between two
stationary states.
h
(3) The angular momentum of this system in a stationary state is an integral multiple of  h .
2
On the basis of these assumptions :
(a) Radius of nth Bohr’s orbit

4  n 2 h2
rn   n2a0
me 2
(b) Velocity of electron

1 e2 V 1 h
Vn   0 
n 4 0 h n n ma 0
(c) Energy of electron in nth orbit,

e2 e2 E 13.6 eV
E  2
  20 =
8 0 rn 8 0 a 0 n n n2
A quanta of light is emitted when an atom in excited state decays to a lower energy state.
h  E f  E i
(d) Frequency, wavelength, wave number of transitions
1  Ef  Ei
 
 c hc

E0  1 1 1 1
  2  2 R 2  2
hc  n i n i   ni nf 

E0
Where R = Rydberg constant = 1.097373 × 107 m–1
hc




[1]

, [2] Modern Physics

X-RAYS
These are electromagnetic wave whose wavelengths typically range from 0.01 to 1 nm.
When an electron strikes a metallic target, before stopping it makes several collisions with atoms. Electrons may
interact with the atom in either of the two ways :
(i) Due to strong nuclear electric field, electron is decelerated. In the process it radiates electromagnetic
energy. Electron emits a series of photons with varying energy. These photons are x-rays. The x-rays
produced in this process are called continuous x-rays.
(ii) When the high energy electron collides with one of the lower shell K electrons in a target atom, if enough
energy can be transfered to this electron, the atom may be ionised. An electron from one of the higher shells
will change its state and fill the inner shell vacancy at lower energy emitting radiation. The emitted radiation
in heavy atoms is x-ray. Photons emitted in this way is called characteristic x-ray.
De Broglie or Matter Waves :
De Broglie proposed that material particles also have both wave and particle properties.
The wavelength to be associated with a particle is given by Planck’s constant divided by the particle’s
momentum.
h

p
This relation for photons was extended to all particles by De Broglie. Waves associated with particles are
called matter waves, and the wavelength is called the de Broglie wavelength of a particle.
 The DeBroglie wavelength of the electron is large enough to be observed. Because of their small mass,
electrons can have a small momentum and in turn a large wavelength.
 If m is the mass and v the velocity of the material particle, then
p = mv
h

mv
 If E is the kinetic energy of the material particle, then

1 2 p2
E  mv 
2 2m

p  2mE
h
Therefore, the de Broglie wavelength is given by  
2mE
 For electrons (me = 9.1 × 10–31 kg)

h 6.62 1034
  m  12.27 A

2mqV 31 19 V
2  9.110 1.6 10 V
Bohr’s Quantisation Condition :
The angular momentum of the electron in this orbit is L = rp. Using the above relation,
nh
L  rp   n h which is Bohr’s quantisation condition.
2
Atomic Nucleus
Nuclear size is of the order of femtometre (1 fm = 10–15 m).