The ground state energy of hydrogen atom is
Question:

The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. The energy of second excited state of $\mathrm{He}^{+}$ion in $\mathrm{eV}$ is:

1.  $-54.4$

2. $-3.4$

3. $-6.04$

4. $-27.2$

Correct Option: , 3

Solution:

According to Bohr’s model energy in $n^{\text {th }}$ state

$=-13.6 \times \frac{Z^{2}}{n^{2}} \mathrm{eV}$

For second excited state, of $\mathrm{He}^{+}, n=3$

$\therefore E_{3}\left(\mathrm{He}^{+}\right)=-13.6 \times \frac{2^{2}}{3^{2}} \mathrm{eV}=-6.04 \mathrm{eV}$