The energy of a hydrogen atom in the ground state is -13.6 eV. The energy of a He⁺ ion in the first excited state will be

-13.6 eV

-27.2 eV

-54.4eV

-6.8 eV

Solution

-13.6 eV

Energy E of an atom with principal quantum number n is given n

$straight E space equals space minus space fraction numerator 13.6 over denominator straight n squared end fraction straight Z squared space for space first space excited space state space straight n space equals space 2 space and space for space He to the power of plus space straight Z space equals space 2 rightwards double arrow space straight E space equals fraction numerator space minus 13.6 space straight x space left parenthesis 2 right parenthesis squared over denominator left parenthesis 2 right parenthesis squared end fraction space equals space minus 13.6 space eV$