Q. An electron makes a transition from an excited state to the ground state of a hydrogen-like atom. Then
NTA AbhyasNTA Abhyas 2022
Solution:
We know that total energy $E$ , potential energy $U$ and kinetic energy $K$ in the $n^{t h}$ orbit is given by
$E=-\frac{13 . 6 z^{2}}{n^{2}}eV$ ,
$U=-2\times \frac{13 . 6 z^{2}}{n^{2}}eV,K=\frac{13 . 6 z^{2}}{n^{2}}eV$
$\therefore U=-2K=2E$
As the total energy decreases with decrease in $n$ , so potential energy decreases and kinetic energy increases with decrease in $n$ .
Hence, when an electron makes a transition from an excited state to the ground state of a hydrogen-like atom, then its kinetic energy increases but potential energy and total energy decrease.
$E=-\frac{13 . 6 z^{2}}{n^{2}}eV$ ,
$U=-2\times \frac{13 . 6 z^{2}}{n^{2}}eV,K=\frac{13 . 6 z^{2}}{n^{2}}eV$
$\therefore U=-2K=2E$
As the total energy decreases with decrease in $n$ , so potential energy decreases and kinetic energy increases with decrease in $n$ .
Hence, when an electron makes a transition from an excited state to the ground state of a hydrogen-like atom, then its kinetic energy increases but potential energy and total energy decrease.