An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the…
An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?
Kinetic energy potential energy and total energy decrease
Kinetic energy and total energy decreased but potential energy increases
Kinetic energy increases but potential energy and total energy decreases
Kinetic energy decreases, potential energy increases but total energy remains the same.
Solution
$\begin{aligned}
& \text { Potential energy }=-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\mathrm{ze}^2}{\mathrm{r}} \\
& \text { Kinetic energy }=-\frac{1}{2}(\text { P.E. })=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{\mathrm{ze}^2}{\mathrm{r}} \\
& \text { Total energy } \left.\frac{1}{2} \text { (P.E. }\right)=-\frac{1}{8 \pi \varepsilon_0} \frac{\mathrm{ze}^2}{\mathrm{r}}
\end{aligned}$
As $r$ decreases K.E, increases but P.E. and T.E. decreases (since they are negative).