Question

An electron in the hydrogen atom is excited from the first orbit to the fifth orbit. The frequency of radiation is:

• A. $0.44\times {10}^{9}Hz$
• B. $0.317\times {10}^{15}Hz$
• C. $6.2\times {10}^{8}Hz$
• D. $1.13\times {10}^{12}Hz$

Answer 1

The correct option is B $0.317\times {10}^{15}Hz$

For hydrogen atom , $Z=1$ and $\Delta E=-13.6[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
$n_1=1$ & $n_2=5$
$\Delta E=-13.6[\frac{1}{5^2}-\frac{1}{1^2}]$
$\Delta E=-13.6[\frac{1}{25}-1]$
$\Delta E$ = $\frac{13.6\times 24}{25}$eV
$\Delta E=h\nu$

& $1eV=1.6\times {10}^{-19}$J
$\therefore \nu =\frac{13.6\times 24}{25\times 6.6\times {10}^{-34}}\times 1.6\times {10}^{-19}=3.17\times {10}^{15}Hz$