Question

A metal was irradiated separately with radiation of wavelength (a) \(400\,\mathrm{nm}\), (b) \(500\,\mathrm{nm}\) and (c) \(600\,\mathrm{nm}\) respectively. Identify the wavelength(s) corresponding to which photoelectrons are emitted from the surface of that metal. \[ \left(\text{Work function}=2.25\,\mathrm{eV},\; h=6.6\times10^{-34}\,\mathrm{J\,s},\; c=3\times10^8\,\mathrm{m\,s^{-1}},\; 1\,\mathrm{eV}=1.6\times10^{-19}\,\mathrm{J}\right) \]

• A. (a) only
• B. (c) only
• C. (a), (b) & (c)
• D. (a) & (b) only

Hint:

The threshold wavelength is \[ \boxed{ \lambda_0=\frac{1240}{\phi(\mathrm{eV})}\ \mathrm{nm} } \] Photoelectric emission occurs only if \[ \boxed{ \lambda<\lambda_0. } \]

Answer 1

The Correct Option is D

Step 1: Find the threshold wavelength. The threshold wavelength is \[ \lambda_0 = \frac{1240}{\phi} = \frac{1240}{2.25} \approx551\,\mathrm{nm}. \] Photoelectric emission occurs only when \[ \lambda<\lambda_0. \]

Step 2: Check each wavelength. For \[ 400\,\mathrm{nm}<551\,\mathrm{nm}, \] photoelectrons are emitted. For \[ 500\,\mathrm{nm}<551\,\mathrm{nm}, \] photoelectrons are emitted. For \[ 600\,\mathrm{nm}>551\,\mathrm{nm}, \] photoelectrons are not emitted. Hence, photoelectric emission occurs for \[ \boxed{\text{(a) and (b) only}.} \] Therefore, \[ \boxed{(D)} \] is the correct answer.