Chapter : 11

What are Dual Nature Of Radiation And Matter ?

Topic Name

Photon Theory of Light

Formula

E = hv=(hc/λ)joule

or E =(hc/λ)

=(1240/λ)eVnm

Symbol Representation

E = Energy of photon,

h = Planck’s constant,

v = Frequency of photon

c = Speed of light

λ = Wavelength of photon

e = Charge of electron

Important Points

  • Packets of energy which are
    emitted by source of radiation
    they travelled in straight line.
  • The rest mass of photon is zero
  • Frequency of photon does not
    change when it passes through
    different medium but its wavelength change.
  • Momentum of photon is (hv/c) or (h/λ)

Intensity of Light

I =(E/At)=(P/A)

I = Intensity of light

E = Incident energy

t = Time taken

A = Area of surface

P = Power of source

  • Energy of light passing through
    per unit area of a surface per
    unit time is known as intensity
    of light.
  • When radiation of suitable
    wavelength or frequency is
    incident on a metal, electrons
    are ejected. This effect is known
    as photoelectric effect.
  • Photoelectric effect varifies
    quantum nature of light.
  • Photoelectric effect is based on
    the law of conservation of
    energy.
  • Alkali metals, like lithium,
    sodium, potassium, caesium etc.
    show photo electric effect with
    visible light.

Work Function

Φ=hvΦ=(hc/λ0)

Φ = Work function

h = Planck’s constant

Vo = Threshold frequency
λo = Threshold wavelength
  • The minimum energy of the
    incident photon below which these will be no ejection of photoelectrons from a metal surface, is known as work
    function or threshold energy
    for that metal.
Topic Name Formula Symbol Representation Important Points
Einstein’s equation of photoelectric effect hv = kmax + Φ0
or
kmax = h – Φ0
or
ev0 = hv – hv0
h = Planck’s constant
v = Frequency of the incident photon
kmax = Maximum kinetic energy of ejected electrons
Φ0 = Work function of the metal
U0 = Stopping potential
V0 = Threshold frequency
e = Charge on electron
• According to Einstein, photon energy is utilized for two purposes, partly for getting the electrons free from the atom and away from the metal surface known as the work function of the metal (Φ0) and the remaining photon energy is used up in providing the electrons kinetic energy of (1/2)mv2
de-Broglie Hypothesis of Matter Waves λ=(h/p)=(h/mv)=(h/√2mE) λ = de-Broglie wavelength or wavelength associated with particle
p = momentum of the particle
m = mass of the moving particle
v = velocity of the moving particle
E = kinetic energy of the moving particle
• According to de-Broglie hypothesis, a moving particle sometimes acts as a wave and sometimes as a particle. The wave associated with waving particle is called matter waves or de-Broglie waves.