Dual Nature of Radiation and Matter Notes Class 12 PDF
Electromagnetic radiation shows the wave nature by exhibiting the phenomena of interference, differaction, and polarisation etc.
also read- 12th Physics Short Question-Answer
Electromagnetic radiation shows the particle nature by exhibiting the phenomena of photo electric effect.
★ Electron emission- The phenomena of emission of election from the surface of a metal is called electron emission.
also read- 12th Physics Notes
Energy of a radiation is in discontinous pockets. These pockets of energy are called quantums or photons.
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# Energy of each quantum (photon) is directly proportional to the frequency of the radiation.
Ε α v
=>E = hv ,where h = Planck's constant = 6.64 × 10⁻³⁴ Js , ν = frequency
# Energy of each photon= E = hν = hc / λ
# Momentum of photon= p =hν / c = h / λ .
# Photon is electrically neutral and its rest mass is zero.
# Photons are not affected by electric and magnetic fields.
# Photon travels with the speed of light in a vaccum.
# Photons can interact with other particles,such as ellectron.
# In a photon-electron collision,both momentum and total energy are conserved.
# Mass of a particle moving with velocity v.
m = m₀ / √(1 - v² / c²)
Where-
m₀ = rest mass of the particles
c = velocity of light
★Threshold frequency- It is denoted by ν₀
Minimum frequency of incident radiation required to make electron just escaped from metal surface is called threshold frequency.
★Work function- It is denoted by ϕ₀
Minimum energy required by an electron to just escape from a metal surface is called work function.
Work function of different metals are different.
ϕ₀ = hν₀
★Einstein's equation of photoelectric effect or
Einstein interpreted photoelectric effect on the basis of planck's quantum theory.According to Einstein, when a light fall on a metal surface then energy of each photon is given to one electron.
If work function of the metal =ϕ₀ = hν₀
mass of electron = m
velocity of electron at metal surface = Vmax
Kinetic energy of election on metal surface = Kmax =½ mv²max
hv =ϕ₀+ Kmax
=> hv=hν₀+ ½ mv²max
=> ½ mv²max= hv-hν₀
=> ½ mv²max= h( v-ν₀)
This is Einstein's photoelectric equation
★Laws of photoelectric effect-
Lenard and Millikon stated following Laws of photoelectric effect on the basis of their experiment.
1. Rate of emission of electrons from a metal surface is directly proportional to the intensity of light falling on it.
2. If, frequency of incident light on a metal surface is below a minimum value then no electron emitts. This minimum frequency is called threshold frequency.
3. Maximum kinetic energy of emitted electrons is directly proportional to the frequency of incident light.
4. The photoelectric emission is instantaneous process. The time lag between incidence of light and emission of photo electrons is less than 10⁻9 sec.
★ Photoelectric cell- This is a device which converts light energy into electrical energy. It is also called electric eye.
Principle- This device is based on photo-electric effect.
Construction- It consists of a vaccumed quartz or glass tube in which there is a cathode C and a wire loop anode A. Which are connected to -ve and +ve terminals of the battery respectively.
Working- when light of suitable frequency falls on the cathode photo-electrons begin to emit. These photo -electrons attracted to-ward anode. Due to which electric Current (Small current) flows through circuit. If no any light incidents on Cathode then photo electrons do not emitt. As a result no any photo-electric current flows through circuit .
Application-
1. In automatic switch on -off of Street lamps .
2. In automatic doors.
3. In burglar on fire alarm
4. In complexion meter
5. In cinema halls, for reproduction off sound.
★ Stopping potential or cutoff potential- It is denoted by ν₀.
Potential difference required to stop photo electric Current is Called stopping potential.
To obtain zero photoelectric current cut-off potential should be able to repell electrons of maximum kinetic energy
also read- 12th board Question Bank
Kmax = eν₀ …i
Now from Einstein photoelectric equation
Kmax= hν-hν₀ ... ii
From equation- i & ii
eν₀= hν- hν₀
ν₀=( h/e ) v- hν₀/e
ν₀=( h/e ) v- ϕ₀/e
This is expression for cutoff potential. When compared from y=mx+c, Graph of ν and ν₀ is an straight line whose slope is h/e.
It can be written ν₀=hc/e( 1/λ-1/ λ₀) .
★ Matter wave or De-brogli wave-
Wave associated with moving particle is called Matter wave or Debrogli wave.
Wave length of material wave. λ=h/p=h/mν
Where-
h= planck's constant
m= mass of moving particle
v= velocity of moving particle
energy of photon= hν
Proof-
energy of photon=hv
mass of moving particle=m
velocity of moving particle=v
E=hν
=> mc2 =h c/ λ [since c= νλ ]
Here c can be replaced by the velocity v of a particle.
=> mν2=hν/ λ
=> mν= h/ λ
=> λ= h/mν= h/p
This is expression for debrogli wave length.
★ Debrogli wavelength of a moving electron-
let an electron of mass m and charge e is accelerated by a potential difference v. Then warkdone by electric field ev will be equal to its kinetic energy.
k=ev ….i
k=½ mv2=p2/2m …..ii
P2 /2m=ev=k
P=√2mk = √2mev
Now , Debrogli wave length
λ= h/p= λ/√2mk=h/√2mev
This is required expression of Debrogli wave length.
Now, putting values of h,m,e
λ=1.227/√v nano-meter
★ Davisson-Germer Experiment-
In 1927, Davisson and Germer experimentally demostrated that moving particles also behave as a wave.
To show this experiment Davisson-Germer obtained suitable wavelength for nickel crystal to accelerate electrons. Then these accelerated electrons are allowed to fall perpendicular on nickel crystal. Now we observe intensity of scattered electron beam at different angle with incident beam. Then it is found that intensity of electron beam at 50 degree with incident beam is maximium. This shows Central maxima of differaction of electron beam.It is a phenomenon of waves. Hence moving particles behave as wave.
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