Question

using photon picture of light show how einstien photoelectric equation can be established.write two features of photoelectric effect which cannot be explained by wave theory

Answer 1

Light consists of photons. When a photon inferacts with an electron it gives its entire energy to the electron and then exists no longer. Energy used to knock out the electron. (hv) is work function and rest energy is given to electron is kE.

(i) Greater intensity has no effect on kE of an electron cannot be explained by wave theory.

(ii) Wave theory also fails to explain the existence of threshold energy.

Answer 2

The Einstein equation of photoelectric effect is $\frac{1}{2}m{V_{\max }} = h\left( {\nu - {\nu _0}} \right)$.

Explanation:

• When the light of frequency more than a specified value falls on metal, the electrons from the metal are emitted.
• This effect is called the photoelectric effect and this specified value of frequency is called the cutoff frequency of that metal.
• The emitted electrons are called photoelectrons.
• If the cutoff frequency of metal is ${\nu _0}$, then, the energy $h{\nu _0}$ ($h$  is Plank's constant) is called the work function of that metal.
• Suppose the light of frequency $\nu$ falls on a metal which has the work function $h{\nu _0}$, then, the possible maximum kinetic energy of a photoelectron by energy conservation is given as

       $\frac{1}{2}m{V_{\max }} = h\left( {\nu - {\nu _0}} \right)$

• This is Einstein’s photoelectric equation.

       Two features of the photoelectric effect are:

• According to the wave theory, the maximum kinetic energy must be increased on increasing the intensity, but it is well proved by the photon theory of light that the kinetic energy is independent of intensity but depends on frequency.
• By wave theory of light, there must be some time interval between the falling of light on the metal and the emission of photo electron while experimentally, no time interval is found.

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