Question

The energy required to transfer an electron from second Bohr orbit to third Bohr orbit in a hydrogen like atom with nuclear charge $Ze$ is $68.0eV.$ The value of $Z$ will be

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is D $6$

Energy required to transfer an electron from second Bohr orbit to third Bohr orbit in a hydrogen atom is
$E_h=\frac{-13.6}{n_2^2}-\frac{-13.6}{n_1^2}$

Since, $n_1=2$ and $n_2=3$,

$E_h=\frac{-13.6}{3^2}-\frac{-13.6}{2^2}$

$E_h=-1.51+3.4$

$E_h=1.89eV$

Now, for the same transfer of an electron in a hydrogen like atom the required energy is:
$E=Z^2\times E_h$

$68=Z^2\times 1.89$

$Z^2=\frac{68}{1.89}$

$Z=\sqrt{\frac{68}{1.89}}$

$Z=\sqrt{3}5.97\approx \sqrt{3}6$

$\Rightarrow Z=6$