An electron in the hydrogen atom initially in the fourth excited state makes a transition to $\mathrm{n}^{ ext {th }}$ energy state by emitting a photon of energy 2.86 eV. The integer value of $n$ will be ____.

Question

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $\mathrm{n}^{	ext {th }}$ energy state by emitting a photon of energy 2.86 eV. The integer value of $n$ will be ____.

Aicharya · Accepted Answer

$\mathrm{E}=13.6\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_1^2}\right)$
$2.86=13.6\left(\frac{1}{\mathrm{n}^2}-\frac{1}{5^2}\right)$
$\begin{aligned} & \frac{1}{\mathrm{n}^2}=0.21+\frac{1}{2.5} \\ & \mathrm{n}^2=4 \\ & \mathrm{n}=2\end{aligned}$

An electron in the hydrogen atom initially in the fourth excited state makes a transition to…

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