Question

An electron revolves round a nucleus of charge $ Ze. 40.8 eV $ of energy is needed to excite an electron from $ n = 1 $ to $ n = 2 $ state. Find the value of $ Z $

• A. $ 2 $
• B. $ 4 $
• C. $ 6 $
• D. $ 8 $

Answer 1

Answer: (A)

Energy of an electron in $n^{th}$ state (or energy level) for a hydrogen like atom,
$E_{n}=\frac{Z^{2}}{n^{2}}\left(E_{1}\right)_{H}$
$=-13.6 \frac{Z^{2}}{n^{2}}eV$
$\therefore $ Energy required to excite electron from
$n=1$ to $n=2$ is $E_{2}-E_{1}$
$\Rightarrow E=-13.6 Z^{2}\left(\frac{1}{2^{2}}-\frac{1}{1^{2}}\right)$
$=13.6 Z^{2}\left(\frac{3}{4}\right)eV $
or $40.8=13.6 z^{2} \left(\frac{3}{4}\right)$
$\Rightarrow Z^{2}=\frac{40.8\times4}{13.6\times3}=4 $
or $Z=2$