In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium…

In the second orbit of hydrogen atom, the energy of an electron is ' $E$ '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium $=2$ )
  1. $\frac{4 \mathrm{E}}{9}$
  2. $\frac{4 \mathrm{E}}{3}$
  3. $\frac{16 \mathrm{E}}{9}$
  4. $\frac{16 \mathrm{E}}{3}$

Solution

$\begin{aligned} & E \propto \frac{Z^2}{n^2} \\ \therefore \quad \frac{E_H}{E_{H e}} & =\frac{\left(Z^2\right)_H}{(n)_H^2} \times \frac{\left(n_{\mathrm{He}}\right)^2}{\left(Z^2\right)_{\mathrm{He}}} \\ & =\frac{1}{2^2} \times \frac{3^2}{2^2}=\frac{9}{16} \\ \therefore \quad E_{H e} & =\frac{16}{9} E_H=\frac{16}{9} E\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

Practice more Structure of Atoms and Nuclei questions on Aicharya