Question

If the wavelength is changed to $4000\stackrel{o}{A}$, the stopping potential will become

• A. 1.36 V
• B. 3.40 V
• C. 1.60 V
• D. 1.98 V

Answer 1

The correct option is D 1.98 V

The Einstein's equation for photoelectric effect is given by $e{V}_0=\frac{hc}{\lambda }-W$ where $V_0=$ stopping potential, $h=$ Planck's constant, $c=$ velocity of light, $\lambda =$wavelength of incident light and $W=$ work function of metal.

Here given , $V_0=1.36V,\lambda =5000\times {10}^{-10}m$

So, $W=\frac{hc}{\lambda }-e{V}_0=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{5000\times {10}^{-10}}-(1.6\times {10}^{-19}\times 1.36)=1.78\times {10}^{-19}J$ The work function is constant for a metal , it does not change when wavelength of incident light is changed.

When wavelength is changed to $4000A^o$, the stopping potential becomes, $V_0^{\prime }=\left(1/e\right)[\frac{hc}{\lambda }-W]=\left(\frac{1}{1.6\times {10}^{-19}}\right)[\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{4000\times {10}^{-10}}-(1.78\times {10}^{-19}\left)\right]=1.98V$