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Q.

When a light of wavelength $\large {{\lambda }_{1}}$ fall on metal sheet will eject electron with V₁ velocity and with $\large {{\lambda }_{2}}$ light eject electron of V₂ velocity. What is $\large V_{2}^{2}-V_{1}^{2}$ value

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a

$\frac{hc}{m}\left( \frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right)\$

b

$\frac{m}{2hc}\left( \frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right)$

c

$\frac{2hc}{m}\left( \frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right)$

d

$\frac{2hc}{m}\left( \frac{1}{{{\lambda }_{1}}}-\frac{1}{{{\lambda }_{2}}} \right)$

answer is A.

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Detailed Solution

$KE=hv-w$

$KE=\frac{hc}{\lambda }-w$

$\frac{1}{2}mv_{1}^{2}=\frac{hc}{{{\lambda }_{1}}}-w$ ... (1)

$\frac{1}{2}mv_{2}^{2}=\frac{hc}{{{\lambda }_{2}}}-w$ ... (2)

eq (2) - eq (1)

$\frac{m}{2}\left( v_{2}^{2}-v_{1}^{2} \right)=\frac{hc}{{{\lambda }_{2}}}-\frac{hc}{{{\lambda }_{1}}}$

$v_{2}^{2}-v_{1}^{2}=\frac{2hc}{m}\left( \frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right)$

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