Q: If the energy of a hydrogen atom in nth orbit is E_{n} , then energy in the nth orbit of a singly ionized helium atom will be

(a) 4 E_{n}

(b) E_{n} / 4

(c) 2E_{n}

(d) E_{n} / 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 $

E_{n}‘ = 4 E_{n}