Question

When is $H_{\alpha }$ line in the emission spectrum of hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.

Answer 1

Energy of an electron in the nth orbit hydrogen atom is given by ,

$E_n=-13.6/n^2$eV

$H_{\alpha }$ line in the emission spectrum of hydrogen atom is obtained in $3\to 2$ transition.

Frequency of photon obtained in the transition is given by:

$\Delta E=hf=-13.6(\frac{1}{9}-\frac{1}{4})eV$

$\Delta E=\frac{13.6\times 5}{36}\times 1.6\times {10}^{-19}J$

$f=\frac{\Delta E}{h}=\frac{13.6\times 5\times 1.6\times {10}^{-19}}{36\times 6.6\times {10}^{-34}}$

$f=4.57\times {10}^{14}Hz$