Question

A sample of hydrogen is bombarded by electrons. Through what potential difference should the electrons be accelerated so that third line of Lyman series be emitted?

• A. $2.55V$
• B. $10.2V$
• C. $12.09V$
• D. $12.75V$

Answer 1

The correct option is D $12.75V$

$hc=1.98644568\times {10}^{25}J.m$

$R=10973731.6m^{-1}$
According to Rydberg formula, (shown in figure)
for third line for lymen series
$\frac{1}{\lambda }=R(1-\frac{1}{4^2})$
$E=\frac{hc}{\lambda }$ $=Rhc(1-\frac{1}{4^2})=2.04\times {10}^{-18}J$

$V=E/q_e=\frac{E}{1.6\times {10}^{-19}}=12.75V$