A photoemissive substance is illuminated with a radiation of wavelength so that it releases electrons with de-Broglie wavelength .

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Solution

Q.
A photoemissive substance is illuminated with a radiation of wavelength $λ_{i}$ so that it releases electrons with de-Broglie wavelength $λ_{e}$ . The longest wavelength of radiation that can emit photoelectron is $λ_{0}$ . Expression for de-Broglie wavelength is given by ( $m$ = mass of the electron, $h$ = Planck's constant and $c$ = speed of light) [2025]

1 $λ_{e} = \sqrt{\frac{h λ_{0}}{2 m c}}$

2 $λ_{e} = \sqrt{\frac{h λ_{i}}{2 m c}}$

3 $λ_{e} = \frac{h}{\sqrt{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$

4 $λ_{e} = \sqrt{\frac{h}{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$

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