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
Revision Notes on Liquids at Rest:-
Force of cohesion:- It is force between two molecules of similar nature.
Force of adhesion:- It is the force between two molecules of different nature.
Molecular range:- The maximum distance between two molecules so that the force of attraction between them remains effective is called molecular range.
Sphere of influence:- Sphere of influence of any molecule is the sphere with molecule as its center and having a radius equal to molecular range (=10-7 cm).
Surface film:- Surface film of a liquid is defined as the portion of liquid lying on the surface and caught between two parallel planes situated molecular range apart.
Surface tension:-
Surface Tension
Surface tension is the property of a liquid by virtue of which its free surface behaves like a stretched membrane and supports, comparatively heavier objects placed over it. It is measured in terms of force of surface tension.
Force of surface tension:- It is defined as the amount of force acting per unit length on either side of an imaginary line drawn over the liquid surface.
(a) T = Force/length = F/l
(b) T = Surface energy/Surface area = W/A
Units:- S.I – Nm-1
C.G.S- dyn cm-1
Additional force:-
(a) For a cylindrical rod:- F = T×2πr (Here r is the radius of cylindrical rod)
(b) For a rectangular block:- F = T×2(l+d) (Here l is the length and d is the thickness of the rectangular block)
(c) For a ring:- F = T×2×2πr (Here r is the radius of cylindrical rod)
Surface energy:-
Potential energy per unit area of the surface is called surface energy.
(a) Expansion under isothermal condition:-
To do work against forces of surface tension:-
W= T×A (Here A is the total increase in surface area)
To supply energy for maintaining the temperature of the film:-
E = T+H
(b) Expansion under adiabatic conditions:-
E = T
Force of surface tension is numerically equal to the surface energy under adiabatic conditions.
Drops and Bubbles:-
(a) Drop:- Area of surface film of a spherical drop of radius R is given by, A = 4πR2
(b) Bubble:- The surface area of the surface films of a bubble of radius R is, A = 2×4πR2
Combination of n drops into one big drop:-
(a) R = n1/3r
(b) Ei = n (4πr2T), Ef =4πR2T
(c) Ef/ Ei = n -1/3
(d) ΔE/Ei = [1-(1/n1/3)]
(e) ΔE = 4πR2T (n1/3-1) = 4πR3T (1/r – 1/R)
Angle of contact:- Angle of contact, for a pair of solid and liquid, is defined as the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid.
(a) When θ < 90º (acute):-
Fa >Fc/√2
(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.
(ii) Liquid molecules will stick with the solid, thus making solid wet.
(iii) Such liquid is put in the solid tube; it will have meniscus concave upwards.
(b) When θ > 90º (obtuse):-Fa<Fc/√2
(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.
(ii) In this case, liquids do not wet the solids.
(iii) Such liquids when put in the solid tube will have a meniscus convex upwards.
(c) When θ = 90º:-?
Fa=Fc/√2
The surface of liquid at the point of contact is plane. In this case force of cohesion and adhesion are comparable to each other.
(d) cosθc = Tsa – Tsl/Tla
Here, Tsa,Tsl and Tla represent solid-air, solid-liquid and liquid-air surface tension respectively). Here θc is acute if Tsl < Tsa while θc is obtuse if Tsl >Tsa.
Capillarity:-
?Rise of Liquid in a Capillary Tube?Capillarity is the phenomenon, by virtue of which the level of liquid in a capillary tube is different from that outside it, is called capillarity.
Weight of liquid, W = Vρg = πr2[h+(r/3)]ρg (Here r is the radius meniscus)
If weight of meniscus is taken into account, the force of surface tension will be,
T = [r(h+(r/3)) ρg]/2 cosθ
For fine capillary, force of surface tension, T = rhρg/2 cosθ
So height, h = 2T cosθ/ rρg