An electron in a hydrogen atom undergoes a transition from an orb… - Vidyadip

Question

An electron in a hydrogen atom undergoes a transition from an orbit with quantum numebr $\mathrm{n}_i$ to another with quantum number $\mathrm{n}_f . \mathrm{V}_i$ and $\mathrm{V}_f$ are respectively the initial and final potential energies of the electon. If $\frac{\mathrm{v}_{\mathrm{i}}}{\mathrm{v}_{\mathrm{f}}}=6.25$, then the smallest possible $n_f$ is

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Answer

$\frac{\mathrm{v}_{\mathrm{i}}}{\mathrm{v}_{\mathrm{f}}}=6.25$

$\Rightarrow\left(\frac{n_f}{n_i}\right)^2=6.25$

$\Rightarrow \frac{\mathrm{n}_{\mathrm{f}}}{\mathrm{n}_{\mathrm{i}}}=2.5=\frac{5}{2}$

$\Rightarrow$ minimum value of $n_f$ is $5$.

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