In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$…

In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$ the energy of an electron will be
  1. $\frac{25 \mathrm{E}}{36}$
  2. $\frac{36 \mathrm{E}}{25}$
  3. $\frac{3 \mathrm{E}}{5}$
  4. $\frac{5 \mathrm{E}}{3}$

Solution

$\mathrm{E} \propto \frac{\mathrm{Z}^2}{\mathrm{n}^2}$ $\begin{aligned} \therefore \quad \frac{E_{\mathrm{H}}}{\mathrm{E}_{\mathrm{He}}} & =\frac{\left(\mathrm{Z}^2\right)_{\mathrm{H}}}{(\mathrm{n})_{\mathrm{H}}^2} \times \frac{(\mathrm{n})_{\mathrm{He}}^2}{\left(\mathrm{Z}^2\right)_{\mathrm{He}}} \\ & =\frac{1}{3^2} \times \frac{5^2}{2^2}=\frac{25}{36} \\ \therefore \quad \mathrm{E}_{\mathrm{He}} & =\frac{36}{25} \mathrm{E}_{\mathrm{H}}=\frac{36}{25} \mathrm{E}\end{aligned}$

Asked in: MHT CET 2024 (02 May Shift 1)

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