Question

In the photoelectric effect (for a given target and a given frequency of the incident light), which of these quantities, if any, depending on the intensity of the incident light beam: (a) the maximum kinetic energy of the electrons, (b) the maximum photoelectric current, (c) the stopping potential, (d) the cut-off frequency?

Short answer

(a) The option is incorrect.

(b) The option is correct.

(c) The option is incorrect.

(d) The option is incorrect.

Step-by-step solution

Introduction:

Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.

Determine the photon energy of sodium light at a wavelength

The number of light rays per unit area is known as the intensity of the light. If the intensity increases, then the no. of photons will also increase. Each photon can release one electron when the energy of each photon is equal to the work function of the metal.

Here, the energy of the photon will not dependent on the intensity of the light.

(a) Maximum kinetic energy of the electrons

Part of the energy of the photon is used to release the electron from metal and the rest is used as the kinetic energy of the electron.

Here, no relation between the intensity and kinetic energy.

Therefore, (a) maximum kinetic energy will not depend on the intensity of light.

(b) The maximum photoelectric current

In terms of photons, a higher amplitude of light means more photons hitting the metal surface. This results in more electrons being ejected in a given time period.

Write the equation for intensity as below.

$I=\frac{nh\nu }{At}$

Here, I is the intensity, n is the number of photons, h is Planck’s constant, is the frequency, A is the area, and t is time.

The intensity is therefore directly proportional to the number of photons and the frequency.

$I\propto n\nu$

You can increase the intensity of the radiation either by increasing the number of photons in it or by increasing the energy of each photon, or both.

In the particle model of light, higher intensity (brighter light) means more photons. Technically, you should say that higher intensity corresponds to more photons passing through a given area in a given time.

The number of electrons (i.e. the electric current) is proportional to the light intensity (at a fixed wavelength) and independent of the frequency of the incident radiation above the threshold value of ${\nu }_0$(no current is observed below ${\nu }_0$).

Hence, (b) the maximum photoelectric current will depend on the intensity of light.

(c) The stopping potential

Stopping is only depending on the kinetic energy of the electron. but kinetic energy will not depend on the instant of light.

Therefore, (c) the stopping potential will not depend on the intensity of light.

(d) The cut-off frequency

The maximum frequency of the incident light to release the electron is known as the cut-off frequency. Frequency depends on the energy of the photon only. But the energy of photons will not depend on the intensity of light.

Therefore, (d) the cut-off frequency will not depend on the intensity of light.

Conclusion

Finally, (b) the maximum photoelectric current will depend on the intensity of light only among all options.