Q: If the energy of a hydrogen atom in nth orbit is En , then energy in the nth orbit of a singly ionized helium atom will be
(a) 4 En
(b) En / 4
(c) 2En
(d) En / 2
Ans: (a)
Sol: Energy of a hydrogen atom in nth orbit is
$\large E_n = -\frac{13.6}{n^2} eV$
Energy in the nth orbit of a singly ionized helium atom is
$\large E_n’ = -\frac{13.6 (2)^2}{n^2} eV$
$\large E_n’ = 4 (-\frac{13.6}{n^2} ) eV $
En‘ = 4 En