Question

The number of photo electrons emitted for light of a frequency $\upsilon$ (higher than the threshold frequency $v_0) $ is proportional to

• A. threshold frequency $(v_0) $
• B. intensity of light
• C. frequency of light (v)
• D. $v-v_0 $

Answer 1

The Correct Option is B

To determine the factor to which the number of photoelectrons emitted is proportional, we need to understand the photoelectric effect. The photoelectric effect is a phenomenon where electrons, known as photoelectrons, are emitted from a material when it is exposed to electromagnetic radiation (light).

According to the photoelectric effect:

1. Each photon has an energy given by $E = hv$, where $h$ is Planck's constant and $v$ is the frequency of the light.
2. The emission of photoelectrons occurs only if the frequency of the light ($v$) is greater than the threshold frequency ($v_0$). This relates to the threshold energy needed to liberate an electron.
3. The kinetic energy of the emitted photoelectrons is given by $E_k = hv - hv_0$. Here, $hv_0$ is the energy needed to liberate an electron (the work function).

Now, let's analyze the options given:

• Threshold frequency $(v_0)$: This affects whether or not photoemission occurs but not the number of photoelectrons emitted.
• Intensity of light: The intensity of light is directly proportional to the number of photons hitting the material. Therefore, it will be proportional to the number of photoelectrons emitted because each photon can potentially liberate one electron.
• Frequency of light (v): A higher frequency increases the energy of individual photons but doesn't affect the number of electrons emitted unless the frequency is less than the threshold.
• $v-v_0$: This determines the kinetic energy of the emitted electrons but does not affect the number of photoelectrons.

Therefore, the correct option is intensity of light, as it determines how many photons are impacting the material surface and consequently, how many electrons are emitted.