Question

An energy of $68\text{eV}$ is required to excite a hydrogen like atom from its second Bohr orbit to the third Bohr orbit. If atomic number of atom is $Z$ and energy required to excite from 1st Bohr orbit to 3rd Bohr orbit is $K,$ then value of $K$ and $Z$ respectively are

• A. $272\text{eV},4$
• B. $435.2\text{eV},4$
• C. $435.2\text{eV},6$
• D. $272\text{eV},6$

Answer 1

The correct option is C $435.2\text{eV},6$

$E=E_0{Z}^2[\frac{1}{n_1^2}-\frac{1}{n_0^2}];E_0=13.6\text{eV}$
$E=E_0{Z}^2[\frac{1}{n_1^2}-\frac{1}{n_0^2}]$
$13.6Z^2[\frac{1}{4}-\frac{1}{9}]=68\therefore Z=6$
Now, $K=13.6Z^2[1-\frac{1}{9}]$
$\Rightarrow K=13.6\times 36\times \frac{8}{9}=\mathrm{4.5.2}\text{eV}$