Question

A 12.9 eV beam of electronic is used to bombard gaseous hydrogen at room temperature.
Upto which energy level the hydrogen atoms would be excite? Calculate the wavelength of the first member of Paschen series and first member of Balmer series.

Answer 1

$n=4$ as energy diff. between $n=1$ and $n=4$ is $12.75eV$.

For first wavelength of Balmer series:

$\frac{hc}{{\lambda }_1}=\left(13.6eV\right)\{\frac{1}{2^2}-\frac{1}{3^2}\}$

$\frac{1240eV.nm}{{\lambda }_1}=13.6\times \frac{5}{36}\Rightarrow {\lambda }_1=\frac{1240\times 36}{5\times 13.6}nm=656.4nm=6564\dot{A}$

For first wavelength of Paschen series:

$\frac{hc}{{{\lambda }^{\prime }}_1}=\left(13.6eV\right)\{\frac{1}{3^2}-\frac{1}{4^2}\}$

$\frac{1240eV.nm}{{{\lambda }^{\prime }}_1}=13.6\times \frac{7}{144}$

$\Rightarrow {\lambda }_1^{\prime }=\frac{1240\times 144}{7\times 13.6}nm=1875.6nm=18756\dot{A}$