Atomic Physics

Atomic Physics

Cathode Rays:

Cathode Rays are streams of fast moving electrons. They can be produced by sing a discharge tube containing gas at a low pressure of order of mm of Hg.

Millikans oil drop experiment

Millikan performed the pioneering oil experiment for the precise measurement of the charge on the electron.

By applying suitable electric field across the metal plates, the charged oil droplets could be caused to rise or fall or down held stationary in the field of view

for sufficiently long time, he found that the charge on an oil droplet was always on integral multiple of on elementary charge 1.6 × 0.2 × 10^-13 C.


Photoelectric Effect

The photoelectric effect is the emission of electrons called photo-electrons when light strikes a surface. To escape from the surface. The electron must

absorb enough energy from the incident radiation to counter the attraction of positive ions in the material of the surface.

Work function(w₀) is the minimum energy of incident radiation, required to eject the electrons from metallic surface is defined as work function of that

surface

w₀ = h₀ =

= Threshold frequency

₀ = Threshold wavelength
Work function in electron volt w₀ (v) =

Note: The photoelectric current is inversely proportional to the square of the distance of the light source from the photo sensitive surface.

When a charge q is accelerated through a potential difference V, the wavelength associated with the charged particle is given by

(a)

(b) In the case of electron,

(c) In the case of proton,

(d) In the case of deuteron,

(e) In the case of a-particle,


X-RAYS:

X-rays are electromagnetic waves with wavelengths ranging from 10 m to 10nm. Most commonly they are produced by the deceleration of high energy electrons bombarding a hard metal target.

X-rays are used as a diagnostic tool in medicine and also for treating certain cancers. As the wavelengths of X-rays are comparable to the lattlice constants

of solid crystals, they are also used to study the crystal structures by diffraction methods.

X-Ray Spectra: As stated above, X-rays are produced by the deceleration of high-energy electrons bombarding a metal target. This would give rise to a

continuous spectrum. This radiation is given the name "bremasstrahlung". But none of the radiation has a wave length shorter than a certain value . This

value corresponds to the maximum energy of the X-ray photon in turn is equal to the maximum KE (= ev) of the striking electrons.

. Here V is accelerating potential in the X-ray tube. However, the x-ray spectrum typically consists of a broad continuous

band and a series of sharp lines which depend on the material used as target. These lines are called characteristic X-rays. Their origin can now be explained on

the basis of the shell structure of the atom.

Louis de Broglie took a bold step and postulated that because photons have both wave and particle characteristics, matter should also have both wave

and particle properties. He suggested that material particles of momentum p should also have wave properties and a corresponding wavelength. A particle of mass

m and moving with a velocity v has a momentum p = mv. The corresponding de Broglie wavelength of the particle is:

It is important to note that, dual nature is not the combination of particle and wave natures. It is completely a new state which can be visualized in the world

of sub-atomic particles only.


Bohr's Atomic Model

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron rounds around a electrons nucleus of positive

charge Z_e (called hydrogen like atom)

He told that on electron in an atom can make around the nucleus in certain circular stable orbits without emitting radiation.

Bohr given that the magnitude of electron's

Angular momentum is quantized

L = mv_n v_n = n

Where r_n = radius of n^th orbit

V_n = corresponding velocity

n = 1, 2, 3, . . .

Corresponding value of orbit radius.

Velocity of electron in n^th orbit given as

v_n = where K =

Similarly radii of orbits

r_n = where = & time period

T_h =

Energy of the Electron: The total energy of the electron in an orbit is made up of the kinetic energy and potential energy. The kinetic energy is given by

Kinetic energy

The potential energy of the electron is due to being in the electric field of the positive nucleus of charge +Ze. The electric potential at a distance r from the

nucleus is given by

The potential energy of the electron of charge -e is therefore

P. E. = V × (_e) =

The total orbital energy E of the electron is thus

En= K. E. + P. E.



When an electron makes transition from higher energy level having energy E₂(n₂) to a lower energy level having energy E₁(n₁) then a photon of frequency n

is emitted.

(a) Energy of emitted radiation

E = E₂ - E₁ =

=

(b) Frequency of emitted radiation

h = E =

(c) Wave number is the number of waves in a unit



The constant outside the bracket is called Rydberg's constant and is denoted by R. Thus



The value of the Rydberg constant is 1.097 × 10⁷ m^-1. The reciprocal of the wavelength is called the wave number , given by




Electron Energy Levels in Hydrogen Atom:

The total energy of the electron in the nth orbit is given by Eqn.



Substituting the numerical values of given constant

we obtain

As 1 electron-volt (eV) =1.6 ×10^-19 J,

we have

The negative sign signifies that the electron is bound to the nucleus by a force of attraction and energy has to be supplied to detach it from the nucleus. The various

energy levels of the electron are

n=1, E₁= _ 13.6 eV. This is the ground state energy

n=2, E₂= _ 3.4 eV. This is the first excited level

n=3, E₃= _ 1.51 eV. This is the second excited level

........ ...................... ...................................
........ ...................... ...................................
=0.The atom is said to be ionised.

The energy level diagram is shown above in Figure which, however, is not drawn to scale.