MHT CET · Physics · Atomic Physics
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?
- A Kinetic energy potential energy and total energy decrease
- B Kinetic energy and total energy decreased but potential energy increases
- C Kinetic energy increases but potential energy and total energy decreases
- D Kinetic energy decreases, potential energy increases but total energy remains the same.
Answer & Solution
Correct Answer
(C) Kinetic energy increases but potential energy and total energy decreases
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \text { Potential energy }=-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\mathrm{ze}^2}{\mathrm{r}} \\
& \text { Kinetic energy }=-\frac{1}{2}(\text { P.E. })=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{\mathrm{ze}^2}{\mathrm{r}} \\
& \text { Total energy } \left.\frac{1}{2} \text { (P.E. }\right)=-\frac{1}{8 \pi \varepsilon_0} \frac{\mathrm{ze}^2}{\mathrm{r}}
\end{aligned}
\)
As \(r\) decreases K.E, increases but P.E. and T.E. decreases (since they are negative).
\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).
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