The ground state energy of a hydrogen atom is -13.6eV. The energy of second excited state of He+ ion in eV is:

A. -27.2

B. -3.4

C. -54.4

D. -6.04

To determine the energy of the second excited state of the He⁺ ion, we can use the formula for the energy levels of hydrogen-like atoms. The energy levels for such ions can be expressed as:

Energy Level Formula

The formula is given by:

E_n = -\frac{Z^2 \cdot 13.6 \text{ eV}}{n^2}

Where:

• E_n is the energy of the nth level.
• Z is the atomic number of the element.
• n is the principal quantum number (energy level).

Applying the Formula to He+

For the He⁺ ion, the atomic number Z is 2. We want to find the energy of the second excited state, which corresponds to n = 3 (since the ground state is n = 1, the first excited state is n = 2, and the second excited state is n = 3).

Calculating the Energy

Now, substituting the values into the formula:

E_3 = -\frac{2^2 \cdot 13.6 \text{ eV}}{3^2}

This simplifies to:

E_3 = -\frac{4 \cdot 13.6 \text{ eV}}{9}

Calculating this gives:

E_3 = -\frac{54.4 \text{ eV}}{9} = -6.04 \text{ eV}

Final Answer

Thus, the energy of the second excited state of the He⁺ ion is -6.04 eV. Therefore, the correct answer is option D.