A gas containing hydrogen-like ions, with atomic number \( Z \), emits photons in transition \( ...

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A gas containing hydrogen-like ions, with atomic number \( Z \), emits photons in transition \( n+2 \rightarrow n \), where \( n=Z \). These photons fall on a metallic plate and eject electrons having minimum de Broglie wavelength \( \lambda \) of \( 5 \AA \). Find the value of \( Z \), if the work function of metal is \( 4.2 \mathrm{eV} \)
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