Question

A $12.5eV$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit :

• A. 2 lines in the Lyman series and 1 line in the Balmar series
• B. 3 lines in the Lyman series
• C. 1 line in the Lyman series and 2 lines in the Balmar series
• D. 3 lines in the Balmer series

Answer 1

Answer: (A)

$E=\frac{hc}{\lambda }\Rightarrow \lambda =\frac{hc}{E}=\frac{6.62\times 10^{-34}\times 3\times 10^8}{12.5\times 1.6\times 10^{-19}}$
$=993A°$
$\frac{1}{\lambda }=R\left(\frac{1}{n_1^2}-\frac{1}{n_{2^2}}\right)$
(where Rydberg constant ,R= 1.097 x $10^7$)
$or,\frac{1}{993\times 10^{-10}}=1.097\times 10^7\left(\frac{1}{1^2}-\frac{1}{n_{2^2}}\right)$
Solving we get $n_2$ = 3
Spectral lines Total number of spectral lines = 3
Two lines in Lyman series for $n_1=1,n_2=2$
and $n_1=1,n_2=3$ and one in Balmer series
for $n_1=2,n_2=3$