Question

The energy of \(He^+\) ion in its first excited state is, (The ground state energy for the Hydrogen atom is – 13.6 eV) :

• A. -13.6 eV
• B. -3.4 eV
• C. -54.4 eV
• D. -27.2 eV

Answer 1

The Correct Option is A

The energy levels for hydrogen-like ions are given by the formula: 

\[ E_n = -\frac{13.6 Z^2}{n^2} \, \text{eV} \]

Here:

• \(Z\) is the atomic number of the ion (for He\(^+\), \(Z = 2\))
• \(n\) is the principal quantum number (the energy level)

For the first excited state, \(n = 2\). Substituting the values:

\[ E_2 = -\frac{13.6 \cdot (2)^2}{(2)^2} \]

Simplify the equation:

\[ E_2 = -13.6 \, \text{eV} \]

Answer

The energy of the He\(^+\) ion in its first excited state is:

\(-13.6 \, \text{eV}\)