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A photo-emissive substance is illuminated with a radiation of wavelength \({\lambda }_{\mathrm{i}}\) so that it releases…

Q1

A photo-emissive substance is illuminated with a radiation of wavelength \({\lambda }_{\mathrm{i}}\) so that it releases electrons with de-Broglie wavelength \({\lambda }_{\mathrm{e}}\). The longest wavelength of radiation that can emit photoelectron is \({\lambda }_{0}\). Expression for de-Broglie wavelength is given by :
( m : mass of the electron, h : Planck's constant and c : speed of light)

a

\({\lambda }_{\mathrm{e}}=\sqrt{\frac{\mathrm{h}}{2\mathrm{mc}\left(\frac{1}{{\lambda }_{\mathrm{i}}}-\frac{1}{{\lambda }_{0}}\right)}}\)

b

\({\lambda }_{e}=\sqrt{\frac{h{\lambda }_{0}}{2mc}}\)

c

\({\lambda }_{e}=\frac{h}{\sqrt{2mc\left(\frac{1}{{\lambda }_{i}}-\frac{1}{{\lambda }_{0}}\right)}}\)

d

\({\lambda }_{e}=\sqrt{\frac{h{\lambda }_{i}}{2mc}}\)

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