Question

Explain the effect of increasing in frequency of incident light on velocity of photoelectron infected

Answer 1

What effect will be seen on a photoelectric current if the frequency doubled?

Photoelectric effect is based on quantum theory of light, which says nothing but, light comes in discrete packets and these packets are called photons.

And, a photon and an electron have a one-to-one relationship(i.e.) one electron will be emitted for one photon, provided that the frequency is greater than the threshold frequency.

The energy of a the incident photon is used up in two ways

i) Work function~Energy required to liberate the electron from the metal surface

ii) The remaining energy of the photon is imparted as kinetic energy

Let me first say why the kinetic energy of the photoelectrons is independent of the intensity of the incident light. When you increase the intensity of the incident light you only increase the number of photons, not their energy. Therefore as mentioned above, (one-to-one relationship), only the number of photons emitted will increase and not their kinetic energy.

Now, coming to the question, The energy of a photon is proportional to its frequency, given by the equation E=hν

We double the frequency, therefore the energy of the photons are doubled (ν′=2ν→E′=2hν). Therefore the kinetic energy imparted is high, which implies the emitted electrons move faster. SO a natural question arises:

As current is defined as the number of electrons crossing a given point per second,increasing their speed must increase the current. But the answer is No, increasing the frequency has ‘no effect’ on photocurrent. (Well , i also found this problem, puzzling for a longtime. But as usual, quora helped:) )

Though increasing the frequency increases the speed, the effect of this increased speed is countered by another factor.

Let 10 electrons pass a given point at a given instant. When you increase the frequency, these electrons are emitted with a greater velocity, But they are more spaced out . This is the key factor, that counters the increase in velocity.