Question

The threshold wavelength for photoelectric from a material is $5200 \times 10^{-10} m$. Photoelectrons will be emitted when this surface is illuminated with monochromatic radiation from
A) 1 W IR lamp
B) 50 W UV lamp
C) 50 W IR lamp
D) 10 W IR lamp

Answer 1

Hint
When a material is illuminated with light, the light interacts with the metal and ejects electrons from the metal. This phenomenon is called the photoelectric effect. The light that is being shined on the metal must have a certain amount of minimum energy to ensure that it can eject electrons from the material.

Complete step by step answer
When light is shined on a material, the light can impart its energy to the electrons inside the material and free them from the material. These electrons are then called photoelectrons. We know that the energy of photons of light are calculated from the formula,
$\Rightarrow E = \dfrac{{hc}}{\lambda }$ where $h$ is the Planck’s constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the photon.
To eject photo-electrons due to the photoelectric effect, the light photons that are illuminating the material must have a certain amount of energy associated with a maximum amount of wavelength that is also known as the threshold wavelength of the material. As the energy of the photon is inversely proportional to the wavelength of the photon, for lower photon wavelengths, the photon will have higher energy and hence, higher tendency of causing the photoelectric effect.
So, since the threshold wavelength of the material is $5200{\text{ }} \times 10^{-10} m$, the photons that are illuminated by this material must have a wavelength lower than the threshold wavelength of the material. $5200{\text{ }} \times 10^{-10} m$ wavelength falls in the visible region of light. From all the options in the question, only UV radiation has a wavelength lower than visible light so only it will be able to eject photo-electrons from the material due to the photo-electric effect.
Hence the correct option is (B).

Note
We’ve also been given the power of different kinds of light in the options but it is not of relevance to the question since the power of the light decides the number of photo-electrons that will be ejected. But the wavelength of the light photons will decide whether photo-electrons will be ejected in the first place.