Question

An electron revolves round a nucleus of charge $Ze.40.8eV$ 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 $E_2-E_1$
$\Rightarrow E=-13.6Z^2\left(\frac{1}{2^2}-\frac{1}{1^2}\right)$
$=13.6Z^2\left(\frac{3}{4}\right)eV$
or $40.8=13.6z^2\left(\frac{3}{4}\right)$
$\Rightarrow Z^2=\frac{40.8\times 4}{13.6\times 3}=4$
or $Z=2$