Question

A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980\mathring{\text{A}}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be: $(hc=12500\text{eV}\mathring{\text{A}})$

• A. $25a_0$
• B. $9a_0$
• C. $16a_0$
• D. $4a_0$

Answer 1

The correct option is C $16a_0$

$\text{Energy of photon},E=\frac{hc}{\lambda }$

$\Rightarrow E=\frac{12500}{980}=12.75\text{eV}$

The energy of the electron in $n^{th}$ orbit is given by

$E_n=\frac{-13.6}{n^2}$

$\Rightarrow E_n-E_1=-13.6[\frac{1}{n^2}-\frac{1}{1^2}]$

$\Rightarrow 12.75=13.6[\frac{1}{1^2}-\frac{1}{n^2}]$

$\Rightarrow n=4$

$\therefore$ Electron will excite to $n=4\to \text{Third excited state}$

The radius of the $n^{th}$ state is given by,

$r_n=n^2{a}_0$

$\Rightarrow r_4=16a_0$

Hence, option $\left(C\right)$ is correct.