Two identical photocathodes

Question:

Two identical photocathodes receive the light of frequencies $f_{1}$ and $f_{2}$ respectively. If the velocities of the photo-electrons coming out are $v_{1}$ and $v_{2}$ respectively, then

  1. $\mathrm{v}_{1}^{2}-\mathrm{v}_{2}^{2}=\frac{2 \mathrm{~h}}{\mathrm{~m}}\left[\mathrm{f}_{1}-\mathrm{f}_{2}\right]$

  2. $\mathrm{v}_{1}^{2}+\mathrm{v}_{2}^{2}=\frac{2 \mathrm{~h}}{\mathrm{~m}}\left[\mathrm{f}_{1}+\mathrm{f}_{2}\right]$

  3. $v_{1}+v_{2}=\left[\frac{2 h}{m}\left(f_{1}+f_{2}\right)\right]^{\frac{1}{2}}$

  4. $\mathrm{v}_{1}-\mathrm{v}_{2}=\left[\frac{2 \mathrm{~h}}{\mathrm{~m}}\left(\mathrm{f}_{1}-\mathrm{f}_{2}\right)\right]^{1 / 2}$

Correct Option: 1

Solution:

(1) $\frac{1}{2} \mathrm{mv}_{1}^{2}=\mathrm{hf}_{1}-\phi$

$\frac{1}{2} \mathrm{mv}_{2}^{2}=\mathrm{hf}_{2}-\phi$

$v_{1}^{2}-v_{2}^{2}=\frac{2 h}{m}\left(f_{1}-f_{2}\right)$

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