Question

If the threshold wavelength of a photoelectric material lies in the green light region, then which one of the following light will not emit photoelectrons?

• A. Ultraviolet
• B. Blue
• C. Violet
• D. Orange
• E. Indigo

Hint:

VIBGYOR: Violet (shortest λ), Indigo, Blue, Green, Yellow, Orange, Red (longest λ). Photoemission requires λ ≤ λ\(_0\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The photoelectric effect is the emission of electrons (photoelectrons) from a material when light shines on it. For this to happen, the energy of the incident light photons must be greater than or equal to the work function of the material. The threshold wavelength (\(\lambda_0\)) is the maximum wavelength of incident light that can cause photoemission. Any light with a wavelength longer than the threshold wavelength will not have enough energy to eject electrons.
Step 2: Key Formula or Approach:
The condition for photoemission is:
Energy of incident photon \(\geq\) Work function (\(\Phi\))
\[ E \geq \Phi \] In terms of wavelength (\(\lambda\)), since \(E = \frac{hc}{\lambda}\), the condition becomes:
\[ \frac{hc}{\lambda} \geq \frac{hc}{\lambda_0} \] This simplifies to:
\[ \lambda \leq \lambda_0 \] So, photoelectrons will be emitted only if the incident wavelength is less than or equal to the threshold wavelength.
Step 2: Detailed Explanation:
We need to compare the wavelengths of the given options with the threshold wavelength, which is in the green region. The order of colors in the visible spectrum from shortest to longest wavelength is given by the acronym VIBGYOR:
Violet< Indigo< Blue< Green< Yellow< Orange< Red
Ultraviolet (UV) light has an even shorter wavelength than violet light.
Given: The threshold wavelength \(\lambda_0\) is in the green region.
We are looking for light that will not emit photoelectrons, which means we need to find light with a wavelength \(\lambda>\lambda_0\) (i.e., \(\lambda>\lambda_{\text{green}}\)).
Let's check the options:
(A) Ultraviolet: \(\lambda_{\text{UV}}<\lambda_{\text{green}}\). Will cause emission.
(B) Blue: \(\lambda_{\text{Blue}}<\lambda_{\text{green}}\). Will cause emission.
(C) Violet: \(\lambda_{\text{Violet}}<\lambda_{\text{green}}\). Will cause emission.
(D) Orange: \(\lambda_{\text{Orange}}>\lambda_{\text{green}}\). Will not cause emission.
(E) Indigo: \(\lambda_{\text{Indigo}}<\lambda_{\text{green}}\). Will cause emission.
Step 3: Final Answer:
Orange light has a longer wavelength than green light, so its photons have less energy than the work function of the material. Therefore, orange light will not emit photoelectrons. This corresponds to option (D).