Question

Consider a hydrogen atom with $\mathrm{v}_{\mathrm{k}}, \mathrm{r}_{\mathrm{k}}$ and $\mathrm{K}_{\mathrm{k}}$ denoting the velocity, orbital radius and kinetic energy of the electron in the $k^{	ext {th }}$ orbit, respectively. The electron undergoes a transition from the $n^{	ext {th }}$ orbit, emitting radiation corresponding to the Lyman series. Considering $h$ to be the Planck's constant and $\epsilon_{0}$ the permittivity of the free space, the correct statement(s) is/are:

Accepted Answer

(A) Magnitude of change in kinetic energy of electron can be expressed as $\frac{\mathrm{h}}{4 \pi}\left|\frac{\mathrm{nv}_{\mathrm{n}}}{\mathrm{r}_{\mathrm{n}}}-\frac{\mathrm{v}_{1}}{\mathrm{r}_{1}}\right|$.; (C) Frequency of the radiation emitted can be expressed as $\frac{\mathrm{e}^{2}}{8 \pi \epsilon_{0} \mathrm{~h}}\left(\frac{1}{\mathrm{r}_{1}}-\frac{1}{\mathrm{r}_{\mathrm{n}}}\right)$.

Answer

(B) Magnitude of change in de Broglie wavelength of the electron can be expressed as $\frac{\mathrm{e}^{2}}{4 \epsilon_{0}}\left|\frac{1}{\mathrm{~K}_{\mathrm{n}}}-\frac{1}{\mathrm{~K}_{1}}\right|$.

Answer

(D) Magnitude of change in total energy of the electron can be expressed as $\frac{\mathrm{h}}{2 \pi}\left|\frac{\mathrm{v}_{1}}{\mathrm{r}_{1}}-\frac{\mathrm{nv}_{\mathrm{n}}}{\mathrm{r}_{\mathrm{n}}}\right|$.

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Modern Physics

Solution

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