Question

A gas absorbs a photon of $355nm$ and emits two wavelength .If one of the emissher ions is at $680nm$,the other is at:

Answer 1

According to law of conservation of energy.
Energy of photon $=$ Total energy of emissher ions
$⟹\frac{hc}{{\lambda }_{photon}}=\frac{hc}{{\lambda }_{emissher}}+\frac{hc}{{\lambda }_{otherion}}$
$⟹\frac{1}{{\lambda }_{photon}}=\frac{1}{{\lambda }_{em}}+\frac{1}{{\lambda }_{Oion}}$
$⟹\frac{1}{335}-\frac{1}{680}=\frac{1}{{\lambda }_{Oion}}$
$⟹{\lambda }_{otherion}=647.50$ $nm$