# Atomic Physics

## Revision Notes on Atomic Physics:-

### e/m of an electron (Thomson Method):

#### (a) e/m of a particle is called the specific charge of the particle.

e/m = v/rB
Here, r is the radius of curvature, B is the strength of magnetic field, v is the velocity, e is the charge on cathode ray particle and m is  the mass.

#### (b) v = E/B

Electric field:- E = V/d
H
Photo electric effect:- Photo-electric effect is the phenomenon of emission of electrons from the surfaces of certain substances, mainly metals, when light of shorter wavelength is incident upon them.
Effect of collector’s potential on photoelectric current:-
(a) Presence of current for zero value potential indicates that the electrons are ejected from the surface of emitter with some energy.
(b) A gradual change in the number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with a variety of velocities.
(c) Current is reduced to zero for some negative potential of collector indicating that there is some upper limit to the energy of electrons emitted.
(d) Current depends upon the intensity of incident light.
(e) Stopping potential is independent of the intensity of light.
Effect of intensity of light:- The photoelectric currentis directly proportional to theintensity of incident radiation.
Effect of frequency of light:-
(a) Stopping potentialdepends upon thefrequency of light. Greater the frequency of light greater is the stopping potential.
(b) Saturation current is independent of frequency.
(c) Threshold frequency is the minimum frequency, that capable of producing photoelectric effect.
Laws of Photoelectricity:-
(a) Photoelectric effect is an instantaneous process.
(b) Photoelectric current is directly proportional to the intensity of incident light and is independent of its frequency.
(c) The stopping potential and hence the maximum velocity of the electrons depends upon the frequency of incident light and is independent of its frequency.
(d) The emission of electrons stops below a certain minimum frequency known as threshold frequency.
Energy contained in bundle or packet:-
E = hf = hc/λ
Here h is the Planck’s constant and f is the frequency.
Work function:- It is defined as the minimum energy required to pull an electron out from the surface of metal. It is denoted by W0.
Einstein’s equation of photoelectric effect:-
(a) ½ mvmax2 = hf – W0
(b) ½ mvmax2 = hf – hf0 = h(f- f0) = h [c/λ – c/λ0]
(c) eV0 = hf – W0
(d)V0 = [(h/e)f] – [W0/e]
Here f0 is threshold frequency.
Threshold frequency (f0):- f0 = work function/h = W/h
Maximum kinetic energy of emitted photo electrons:-
?Kmax= ½ mvmax2 = eV0
Threshold wavelength:- λ0 = c/f0 = hc/hf0 = hc/W
Slope of V0~ v graph:- Slope= h/e
Rest mass of photon = 0, Charge = 0
Energy of photon:- E = hf = hc/λ
Momentum of photon:- p = E/c = h/λ = hf/c
Mass od photon:- m = E/c2 = h/cλ = hf/c2
For electron, λe = [12.27/√V]Å
For proton, λp = [0.286/√V]Å
For alpha particle, λα = [0.286/√V]Å
For particle at temperature T, λ = h/√3mKT   (E = 3/2 KT)
The wavelength of electron accelerated by potential difference of V volts is:-
λe= [12.27/√V]Å

#### Number of photons:-

(a) Number of photons per sec per m2, np = Intensity/hf
(b) Number of photons incident per second, np = Power/hf
(c) Number of electrons emitted per second = (efficiency per surface)× (number of photons incident per second)
Compton wave length:-
(a) λc = h/m0c
Here h is the Planck’s constant, m0 is the rest mass of electron and c is the speed of light.
(b) Change in wavelength:- λ’ – λ =λc (1-cos?)
de Broglie wavelength (λ):-λ = h/mv = h/√(2mE) = h/√(2meV)
In accordance to Bohr’s postulate of atomic structure, the angular momentum of an electron is an integral multiple of h/2π.
So, mvr = nh/2π
Bragg’s diffraction law:- 2dsinθ = nλ
Here λ is the wavelength of electron and d is distance between the planes.
Rutherford’s atomic model (α-particle scattering):-
(a) N(θ) ∝ cosec4(θ/2)

# Liquid in Rest

#### For fine capillary, force of surface tension, T = rhρg/2 cosθ

So height, h = 2T cosθ/ rρg