Question

In a hydrogen atom, the energy of an electron in an orbit is - 3.4 eV. When it is excited to the next higher energy level and comes back to ground state, calculate the wave length of emitted radiation.

• A. $9\times {10}^{-7}m$
• B. $9\times {10}^{-9}m$
• C. $9A^o$
• D. none of these

Answer 1

The correct option is D none of these

$-13.6\frac{z^2}{n^2}=$Energy

$-3.4=\frac{-13.6}{n^2}\Rightarrow n=2$

First it is excited from $n=2$ to $n=3$ and brought back to ground level. To calculate $Z_{3\to 1}$

$\frac{1}{Z_{3-1}}=R_H(1-\frac{1}{9})=\frac{8R_H}{9}{Z}_{3\to 1}=\frac{9}{8R_H}=1012\times {10}^{-10}m=1.012\times {10}^{-7}m\frac{1}{R_H}=912A^{\bullet }$

To calculate $Z_{2\to 3}$

$\frac{1}{Z_{2\to 3}}=R_H(\frac{1}{4}-\frac{1}{9})=\frac{5R_H}{36}{Z}_{2\to 3}=6.556\times {10}^{-7}m$.