Question

The ionisation energy of second electron in helium atom is

• A. $100eV$
• B. $27.2eV$
• C. $13.6eV$
• D. $54.4eV$

Answer 1

The correct option is D $54.4eV$

The helium ground state consists of two identical 1s electrons. After one electron is removed we get the $He+$ ion. The $He+$ ion is just like a hydrogen atom with two units of charge in the nucleus. The energy of the remaining helium electron should be $4\times (-13.6eV)=-54.4eV$ as observed.
Energy required to remove the second electron is $54.4eV$, as it is modelled like the hydrogen levels. Since the hydrogenic energy levels depend upon the square of the nuclear charge we get the given energy.