Question

When photons of energy \(4.2\,\text{eV}\) incident on a photosensitive material of work function \(2.2\,\text{eV}\), photoelectrons are emitted with a maximum linear momentum of \(P\). If photons of energy \(6.2\,\text{eV}\) incident on the same photosensitive material, the maximum linear momentum of the emitted photoelectrons is

• A. \(4P\)
• B. \(P\sqrt{2}\)
• C. \(2P\)
• D. \(P\sqrt{3}\) \bigskip

Hint:

In photoelectric effect, \[ K_{\max}=E_{\text{photon}}-\phi. \] Since \[ p=\sqrt{2mK_{\max}}, \] the maximum momentum is proportional to the square root of the maximum kinetic energy: \[ p\propto \sqrt{K_{\max}}. \]

Answer 1

The Correct Option is B

Concept: Einstein's equation: \(K_{\max} = h\nu - \phi\). Momentum \(p \propto \sqrt{K_{\max}}\).

Step 1: Case 1: \(K_1 = 4.2 - 2.2 = 2\) eV, momentum \(P\). Case 2: \(K_2 = 6.2 - 2.2 = 4\) eV. \(p_2/P = \sqrt{4/2} = \sqrt{2} \Rightarrow p_2 = P\sqrt{2}\).

Step 2: Write the final answer. \(\boxed{p_2=P\sqrt{2}}\)