Modern Physics 1 Question 14
11. As an electron makes a transition from an excited state to the ground state of a hydrogen like atom/ion
(2015 Main)
(a) kinetic energy, potential energy and total energy decrease
(b) kinetic energy decreases, potential energy increases but total energy remains same
(c) kinetic energy and total energy decrease but potential energy increases
(d) its kinetic energy increases but potential energy and total energy decrease
Show Answer
Solution:
- The expressions of kinetic energy, potential energy and total energy are
and
$$ \begin{aligned} & K _n=\frac{m e^{4}}{8 \varepsilon _0^{2} n^{2} h^{2}} \quad \Rightarrow \quad K _n \propto \frac{1}{n^{2}} \\ & U _n=\frac{-m e^{4}}{4 \varepsilon _0^{2} n^{2} h^{2}} \quad \Rightarrow \quad U _n \propto-\frac{1}{n^{2}} \\ & E _n=\frac{-m e^{4}}{8 \varepsilon _0^{2} n^{2} h^{2}} \quad \Rightarrow \quad E _n \propto-\frac{1}{n^{2}} \end{aligned} $$
In the transition from some excited state to ground state value of $n$ decreases, therefore kinetic energy increases, but potential and total energy decreases.
