Question

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. $4E_{n}$
• B. $E_{n}/4$
• C. $2E_{n}$
• D. $E_{n}/2$

Answer 1

Answer: (A)

$4E_{n}$

Answer 2

The energy of the electron in the $n^{th}$ orbit is
$E = E \propto Z^2 \frac {1}{n^2}$
Given, $Z_H=1,Z_{He}=2$
$\therefore \frac {E_H}{E_{He}}= \frac {Z_H^2}{Z^2_{He}}= \frac {1}{4}$
$\Rightarrow E_{He}=4 E_H$
Given, $E_H=E_n$
$\therefore E_{He}=4E_n$