What is the energy associated with first orbit of $\mathrm{He}^{+}$?

What is the energy associated with first orbit of $\mathrm{He}^{+}$?
  1. $\quad-2.18 \times 10^{-18} \mathrm{~J}$
  2. $-4.36 \times 10^{-18} \mathrm{~J}$
  3. $-6.54 \times 10^{-18} \mathrm{~J}$
  4. $-8.72 \times 10^{-18} \mathrm{~J}$

Solution

For the first orbit of monopositive $\mathrm{He}^{+}$ion, $\begin{aligned} & Z=2, n=1 \\ & E_n=-2.18 \times 10^{-18}\left(\frac{Z^2}{n^2}\right) J \\ \therefore \quad & E_1=-2.18 \times 10^{-18}\left(\frac{2^2}{1^2}\right)=-8.72 \times 10^{-18} \mathrm{~J} \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

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