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Q.
The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statement is true ?
IIT JEEIIT JEE 2000
Solution:
$v_n \propto \frac{1}{n} \therefore KE\propto \frac{1}{n^2}$ (with positive sign)
Potential energy U is negative and $U_n\propto \frac{1}{r_n}$
$\bigg[U_n=-\frac{1}{4\pi\varepsilon_0}.\frac{Ze^2}{r_n}\bigg]$
$\propto \frac{1}{n^2}$ (because $r_n\propto n^2$)
Similarly total energy $E_n\propto \frac{1}{n^2}$ (with negative sign)
Therefore, when an electron jumps from some excited state to the ground state, value of n will decrease. Therefore, kinetic energy will increase (with positive sign), potential energy and total energy will also increase but with negative sign. Thus, finally kinetic energy will increase, while potential and total energies will decrease.