Question

The kinetic energy of photoelectrons depends on?

• A. The intensity of incident light
• B. The sum of threshold frequency and frequency of incident light
• C. The ratio of of threshold frequency and frequency of incident light
• D. The difference of threshold frequency and frequency of incident light

Answer 1

The correct option is D

The difference of threshold frequency and frequency of incident light

The explanation for the correct option:

Option (D): The difference between threshold frequency and frequency of incident light

1. The photoelectric effect is related to the incident light frequency $\left(\mathrm{\nu }\right)$ by the following equation:
   ${\mathrm{E}}_{\mathrm{k}}={\mathrm{eV}}_{\mathrm{s}}=\mathrm{h\nu }-\mathrm{\varphi },$
   where $\mathrm{\varphi }={\mathrm{h\nu }}_0$​ is denoted as the material's work function and ${\mathrm{E}}_{\mathrm{k}}$​ is known as the kinetic energy of the photoelectron.
2. Thus, ${\mathrm{E}}_{\mathrm{k}}=\mathrm{h\nu }-{\mathrm{h\nu }}_0,\mathrm{where}{\mathrm{\nu }}_0$​ is denoted as the threshold frequency for the metal.
   $\Rightarrow {\mathrm{E}}_{\mathrm{k}}=\mathrm{h}(\mathrm{\nu }-{\mathrm{\nu }}_0)$
3. So from the given equation, we can conclude that the kinetic energy of photoelectrons depends on the difference between threshold frequency and frequency of incident light.

The explanation for the incorrect option:

Option (A): The intensity of incident light

1. The intensity of incident light generally only gives us an idea about the number or the intensity of the emitted photoelectrons.
2. When the intensity of incident light increases, it means that number of photons and emitted photoelectrons increases in incident light.
3. The kinetic energy of photoelectrons usually doesn't depend on the intensity of incident light.
4. Hence the given option doesn't coincide with the correct option.

Option (B): The sum of threshold frequency and frequency of incident light

1. The kinetic energy of photoelectrons usually depends on the difference between threshold frequency and frequency of incident light and not on the sum of threshold frequency and frequency of incident light.
2. Thus, the given option is the incorrect one.

Option (C): The ratio of threshold frequency and frequency of incident light

1. The kinetic energy of photoelectrons depends on the difference between threshold frequency and frequency of incident light.
2. The ratio of threshold frequency and frequency of incident light doesn't explain the kinetic energy of photoelectrons.
3. Hence the given option doesn't represent the correct option.

Hence, option D is correct.