Question

Two identical photo cathodes receive light of frequencies $f_1$ and $f_2$. if the velocities of the photoelectrons (of mass m) coming out are respectively $v_1$ and $v_2$, then

• A. $v^{2}_{1}-v^{2}_{2}=\frac{2h}{m}\left(f_{1}-f_{2}\right)$
• B. $v_{1}+v_{2}=\left[\frac{2h}{m}\left(f_{1}+f_{2}\right)\right]^{1/ 2}$
• C. $v^{2}_{1}-v^{2}_{2}=\frac{2h}{m}\left(f_{1}+f_{2}\right)$
• D. $v_{1}-v_{2}=\left[\frac{2h}{m}\left(f_{1}-f_{2}\right)\right]^{1/ 2}$

Answer 1

Answer: (A)

$\frac{1}{2}m\left(v^{2}_{1}-v^{2}_{2}\right)=h\left(f_{1}-f_{2}\right)$
$\Rightarrow v^{2}_{1}-v^{2}_{2}=\frac{2h}{m}\left(f_{1}-f_{2}\right).$