Question

Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively illuminate a metallic surface whose work function is 0.5 eV successively. Ratio of maximum speed of emitted electrons will be :

• A. 1:4
• B. 1:2
• C. 1:1
• D. 1:5

Answer 1

The correct option is B 1:2

$K_{max}=E-\varphi$

$K_{ma{x}_1}=1eV-0.5eV=0.5eV$

$K_{ma{x}_2}=2.5eV-0.5eV=2eV$

Also $V_{max}=\sqrt{\frac{2K_{max}}{m}}\Rightarrow V_{max}\propto \sqrt{K_{max}}$

$\Rightarrow \frac{V_{ma{x}_1}}{V_{ma{x}_2}}=\sqrt{\frac{K_{ma{x}_1}}{K_{ma{x}_2}}}=\frac{1}{2}$