Question

Transition of an electron takes place between two energy levels differing in energy by $△E$ eV. The wavelength of the emitted spectral line is approximately

• A. $\frac{12375}{△E}\times {10}^{-4}m$
• B. $\frac{12375}{△E}\times {10}^{-6}m$
• C. $\frac{12375}{△E}\times {10}^{-8}m$
• D. $\frac{12375}{△E}\times {10}^{-10}m$

Answer 1

The correct option is D $\frac{12375}{△E}\times {10}^{-10}m$

$\begin{array}{c}\text{given -}\\ \text{Energy difference}=\Delta E\text{ev.}\\ \Delta E=h\nu =\frac{hC}{\lambda }\\ \lambda =\frac{hC}{\Delta E}=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{\Delta E\times 1.6\times {10}^{-19}}m.\\ =\frac{12.375}{\Delta E}\times {10}^{-7}m.\\ =\frac{12375}{\Delta E}\times {10}^{-10}m.\end{array}$