Question

Which energy level of $He ^{+}$ 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 $He ^{+}, E_{n}=\frac{E_{1} \times 2^{2}}{n^{2}}$

As given, $\frac{E_{1} \times 2^{2}}{n^{2}}=E_{1}$

$\therefore n=2$

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