Question

The binding energy of $e^{-}$ in the ground state of the hydrogen atom is $13.6eV$. The energies required to eject out an electron from three lowest states of H$e^{+}$ atom will be (in eV):

• A. $13.6,10.2,3.4$
• B. $13.6,3.4,1.5$
• C. $13.6,27.2,40.8$
• D. $54.4,13.6,6$

Answer 1

The correct option is D $54.4,13.6,6$

The binding energy of $e^{-}$ in the ground state of the hydrogen atom is 13.6 eV. The energies required to eject out an electron from three lowest states of H, $e^{+}$ atom will be (in eV) 54.4, 13.6, 6 respectively.

The energy is proportional to $\frac{Z^2}{n^2}$.

The ground state energy of H atom $E=13.6eV$.

The energy required to eject out an electron from the first lowest state of He+ is

$E_1=\frac{Z^2}{n^2}E=\frac{2^2}{1^2}13.6=54.4$.
The energy required to eject out an electron from the second-lowest state of He+ is

$E_2=\frac{Z^2}{n^2}E=\frac{2^2}{2^2}13.6=13.6$.
The energy required to eject out an electron from the third-lowest state of He+ is

$E_3=\frac{Z^2}{n^2}E=\frac{2^2}{3^2}13.6=6$.

Hence, the correct option is $D$