Question 23: Dual Nature of Matter and Radiation

Question

In the photoelectric experiment, the frequency of the incident radiation is doubled. What will be its effect on the photoelectric current?

Accepted Answer

The photoelectric effect is a phenomenon where electrons are ejected from the surface of a material (usually metals and semiconductors) when light of sufficient frequency shines on it. The basic relationship governing the photoelectric effect is given by Einstein's equation:
$$E_k = h
u - \phi$$
where $E_k$ is the kinetic energy of the ejected electrons, $h$ is Planck's constant ($6.626 	imes 10^{-34} \, 	ext{m}^2 \, 	ext{kg} / 	ext{s}$), $
u$ is the frequency of the incident radiation, and $\phi$ is the work function of the material, which is a measure of the minimum energy required to eject electrons from the material's surface.
When the frequency of the incident radiation is doubled, it means that the energy of the photons being incident on the material is also increased since the energy of a photon is directly proportional to its frequency ($E = h
u$). This increase in photon energy will increase the kinetic energy of the ejected electrons if the frequency of the incident light is above the threshold frequency required to overcome the work function.
However, the increase in the frequency of the incident radiation does not necessarily increase the photoelectric current directly. The photoelectric current is related to the number of photoelectrons ejected per unit time, which, in turn, depends on the intensity of the incident light (i.e., the number of photons hitting the surface per unit time) and not directly on the energy (or frequency) of the individual photons. Assuming the intensity of the incident light and all other conditions remain constant, doubling the frequency of the incident radiation, which increases the energy of individual photons, will not directly affect the number of electrons being ejected per unit time, provided the original frequency was already above the threshold frequency.
What may change, given a higher frequency (and therefore higher energy photons), is the maximum kinetic energy of the ejected electrons, but this does not directly translate to a change in photoelectric current unless the increase in energy results in a significantly greater efficiency in electron ejection, which is not a given in this scenario. Therefore, based on the options provided and the assumption that the intensity and other factors remain constant:
Option C: Photoelectric current will not change.
This option is the most accurate given that the statement does not imply any change in the number of photons (intensity) hitting the surface but rather only their energy (frequency). The actual effect on the photoelectric current would depend on more details not provided in the question, such as the relationship between photon energy and the efficiency of electron ejection beyond the threshold frequency requirement.

Answer

Photoelectric current will be halved

Answer

Photoelectric current will be doubled

Answer

Photoelectric current will not change.

Answer

Photoelectric current will become zero

Dual Nature of Matter and Radiation

In the photoelectric experiment, the frequency of the incident radiation is doubled. What will be its effect on the photoelectric current?

Choose the correct answer: