Question

Maximum kinetic energy of electrons emitted in photoelectric effect increases when
A. Intensity of light is decreased
B. Light source is brought nearer the metal
C. Frequency of light is decreased
D. wavelength of light is decreased

Answer 1

In case of photoelectric effect, the cathode is hit by a beam of photons which causes electrons in cathode to come out of the cathode and go to anode. Potential difference is maintained between cathode and anode. The intensity of the incident light determines the current and the energy of the incident light determines the maximum energy of the electron.

Formula used:
$E = \dfrac{{hc}}{\lambda } - \phi$

Complete step by step answer:
When radiation is hit on the cathode some of the energy of that radiation will be used by the electron to come out of that electrode which is called a work function and the remaining energy is used as a kinetic energy to reach the anode. When an electron reaches anode automatically current is generated. The amount of current produced depends on the intensity of the radiation.
We can assume that each photon will bring one electron out of the metal. Hence ‘n’ photons will bring ‘n’ electrons out of the metal.
Now some energy from the photon is used as a work function to remove electrons from the metal and the rest will be the remaining energy. Hence the maximum energy of an electron will be
$E = \dfrac{{hc}}{\lambda } - \phi$
Where $\phi$ is the work function and ‘h’ is the planck's constant and $\lambda$ is the wavelength of the light and ‘c’ is the velocity of light and ‘E’ is the maximum kinetic energy.
Work function will be constant for a metal and as the wavelength of light decreases the energy of radiation increases and the maximum kinetic energy of the photoelectron emitted increases.
Hence option D will be the correct answer.

Note:
This maximum kinetic energy determines the stopping potential. It means the potential maintained at anode relative to cathode such that no electron reaches the anode. It doesn’t matter if we increase the number of photons, but as long as the photon energy is less than the required work function, the electron will not emit from the metal. If we apply the stopping potential at the anode then no electron will reach the anode and there will be no photoelectric current.