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  4. The kinetic energy of emitted electron is E when the light incident on the metal has wavelength λ. To double the kinetic energy, the incident light must have wavelength :

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Q. The kinetic energy of emitted electron is $E$ when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength :

JEE MainJEE Main 2022Dual Nature of Radiation and Matter

Solution:

$ E =\frac{ hc }{\lambda}-\phi-( i ) $
$ 2 E =\frac{ hc }{\lambda^{\prime}}-\phi-(\text { ii) }$
(ii) - (i)
$E = hc \left(\frac{1}{\lambda^{\prime}}-\frac{1}{\lambda}\right) $
$ \Rightarrow \lambda^{\prime}=\frac{ hc \lambda}{ E \lambda+ hc }$