A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980 Ã…$. The…
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980 Ã…$. The radius of the atom in the excited state, in terms of Bohr radius $a_{0}$, will be:
$25 \mathrm{a}_{0}$
$9 a_{0}$
$16 \mathrm{a}_{0}$
None of the above
Solution
Energy of photon $=\frac{\mathrm{hc}}{\lambda}=\frac{12500}{980}=12.75 \mathrm{eV}$
Energy of electron in $\mathrm{n}^{\text {th }}$ orbit is given by
$\mathrm{En}=\frac{-13.6}{\mathrm{n}^{2}} \Rightarrow \mathrm{E}_{\mathrm{n}}-\mathrm{E}_{1}=-13.6\left[\frac{1}{\mathrm{n}^{2}} \frac{-1}{1^{2}}\right]$
$\Rightarrow 12.75=13.6\left[\frac{1}{1^{2}} \frac{-1}{\mathrm{n}^{2}}\right] \Rightarrow \mathrm{n}=4$
$\therefore$ Electron will excite to $\mathrm{n}=4$ We know that ' $R^{\prime} \propto n^{2}$
$\therefore$ Radius of atom will be $16 \mathrm{a}_{0}$