1. Tardigrade
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  4. Given that a photon of light of wavelength 10,000Å has an energy equal to 1.23eV . When light of wavelength 5000Å and intensity I0 falls on a photoelectric cell, the surface current is 0.40× 10- 6A and the stopping potential is 1.36V , then the work function is

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Q. Given that a photon of light of wavelength $10,000Å$ has an energy equal to $1.23eV$ . When light of wavelength $5000Å$ and intensity $I_{0}$ falls on a photoelectric cell, the surface current is $0.40\times 10^{- 6}A$ and the stopping potential is $1.36V$ , then the work function is

NTA AbhyasNTA Abhyas 2022

Solution:

$E=\frac{h c}{\lambda }$ or $E \propto \frac{1}{\lambda } \, \therefore \, \frac{E_{2}}{E_{1}}=\frac{\lambda _{1}}{\lambda _{2}}$
or $E_{2}=E_{1}\times \frac{\lambda _{1}}{\lambda _{2}}=1.23\times \frac{10,000}{5,000}=2.46 \, eV$
Now, $hv-\phi_{0}=\frac{1}{2}mv_{m a x}^{2}=eV_{s}$
$\Rightarrow \phi_{0}=hv_{2}-eV_{s}=E_{2}-eV_{s}$
$=2.46-1.36=1.10 \, eV$