Question

A hydrogen-like neutral species is in some excited state $A$ . On absorbing a photon of energy $3.066\,eV$ , it gets excited to a new state $B$ . When the electron from state $B$ returns back, photons of a maximum ten different wavelengths can be observed in which some photons are of energy smaller than $3.066\,eV$ , some are of equal energy and only four photons are having energy greater than $3.066\,eV$ . The ionization energy of this atom is

• A. $14.6\,eV$
• B. $3.066\,eV$
• C. $6.132\,eV$
• D. $9.2\,eV$

Answer 1

Answer: (A)

The maximum number of photons emitted during de-excitation is,
$\frac{n \left(n - 1\right)}{2}=10 \, \, \Rightarrow n=5$
As the atom is in an excited state, $n=1$ can't be possible.
For the maximum energy photon, the transition must be from $n=5$ to $n=2$ .
$\Rightarrow $ $kZ^{2}\left(\frac{1}{2^{2}} - \frac{1}{5^{2}}\right)=3.066$ $eV$
$\Rightarrow $ $kZ^{2}=14.6 \, eV$
Ionisation energy is $14.6 \, eV$ .
For $n=5$ to $n=1$ transition, photon energy is more than $3.066\,eV$