Question

All electrons ejected from a surface by incident light of wavelength 200 nm can be stopped before traveling 1 m in the direction of a uniform electric field of $4N{C}^{-1}$. The work function of the surface is

• A. 4 eV
• B. 6.2 eV
• C. 2 eV
• D. 2.2 eV

Answer 1

The correct option is D 2.2 eV

The Einstein's equation for photoelectric effect is $e{V}_0=\frac{hc}{\lambda }-W$

where $V_0=$ stopping potential, $\lambda =$ wavelength of incident light, $W=$ work function of metal.

Here, $V_0=E/d=4/1=4$ volt, $\lambda =200nm=200\times {10}^{-9}m$

Thus, $W=\frac{hc}{\lambda }-e{V}_0=\frac{(6.62\times {10}^{-34})(3\times {10}^8)}{200\times {10}^{-9}}-(1.6\times {10}^{-19})4=3.53\times {10}^{-19}J=2.2eV$

as $(1eV=1.6\times {10}^{-19}J)$