Question

In a hydrogen like species, electron is in $2^{nd}$ excited state. The binding energy of $4^{th}$ state of this species is $13.6eV$, then:

• A. a $25eV$ photon can set free the electron from the second excited state of this sample
• B. $3$ different types of photon will be observed if electron make transition up to ground state from the second excited state
• C. if $23eV$ photon is used for electron is $2^{nd}$ excited state then $K.E.$ of the ejected electron is $1eV$
• D. $2^{nd}$ line of Balmer series of this sample has same energy value as the energy required for excitation of $H$ atom from ground to $1^{st}$ excited state

Answer 1

The correct option is A a $25eV$ photon can set free the electron from the second excited state of this sample

We know that $E=13.6\times \frac{z^2}{n^2}$

$13.6=13.6\times \frac{2^2}{4^2}$

$z=4$

$\therefore$ Species is Berellium $E$ (for $n=3$) $13.6\times \dfrac{4^{2}}{3^{2}}= 24.177\simeq 25$

$\therefore 25eV$ photon can set free electron from 2${}^{nd}$ excited state.

Hence, the correct option is $\text{A}$