Question

An electron in an atom absorbs radiation of wavelength 392.n.m and later on it emits energy in the from of photons of two different wavelengths. If one of the wavelength is 712 n.m. Calculate the other.

Answer 1

Given,

Energy, $E=\frac{hc}{\lambda }$ (where, $\lambda$ is wavelength)

Energy absorbed wavelength,$\lambda =392nm$

One wave length is ${\lambda }^{\prime }=712nm$

From conservation of energy.

Energy absorbed by electron = Energy emitted in first wave + Energy emitted in second wave

$\frac{hc}{\lambda }=\frac{hc}{{\lambda }^{\prime }}+\frac{hc}{{\lambda }^{\prime \prime }}$

${\lambda }^{\prime \prime }=\frac{{\lambda }^{\prime }\times \lambda }{{\lambda }^{\prime }-\lambda }=\frac{712\times 392}{712-392}=872.2nm$

Hence, second wavelength is $872.2nm$