Question

Two radiations of photons energies $1 \,eV$ and $2.5\, eV$, successively illuminate a photosensitive metallic surface of work function $0.5 \,eV$. The ratio of the maximum speeds of the emitted electrons is

• A. $1: 4$
• B. $1: 2$
• C. $1: 1$
• D. $1: 5$

Answer 1

Answer: (B)

According to Einsten's photoelectric effect, the K.E. of the radiated electrons
$K \cdot E_{\max }=E-W$
$\frac{1}{2} m v_{1}^{2}=(1-0.5) e V=0.5 \,eV$
$\frac{1}{2} m v_{2}^{2}=(2.5-0.5) eV =2\, eV $
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{0.5}{2}}=\frac{1}{\sqrt{4}}=\frac{1}{2}$