Show that ground state energy of an electron in H-atom is equal to the first excited state energy of electron in `He^+` ion (assuming their Rydberg's constants to be equal ).

Explanation

To show that the ground state energy of an electron in the hydrogen atom (H) is equal to the first excited state energy of an electron in the helium ion (He⁺), we will use the formula for the energy levels of hydrogen-like atoms.

### Step 1: Write the formula for the energy levels of hydrogen-like atoms.
The energy of an electron in the nth orbit of a hydrogen-like atom is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number.
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