Question

Which energy level of $H{e}^{+}$ has energy equal to ground state energy of H-atom?

• A. $1^{\text{st }}$
• B. $2^{\text{nd }}$
• C. $3^{\text{rd }}$
• D. $4^{\text{th }}$

Answer 1

Answer: (B)

$E_n$ for any one electron species $=\frac{E_1\times Z^2}{n^2}$ where $E_1$ is ground state energy of $H$ -atom.

For $H{e}^{+},E_n=\frac{E_1\times 2^2}{n^2}$

As given, $\frac{E_1\times 2^2}{n^2}=E_1$

$\therefore n=2$

Thus, $2^{\text{nd }}$ energy level of $H{e}^{+}$ has energy equal to ground state energy of $H$ -atom.