2001 AIPMT AtomsEnergy Levels of Hydrogen-like Atoms Easy Question 52 of 55 in Atoms

The energy of hydrogen atom in nth orbit is $E_n$ then the energy in nth orbit of singly ionised helium atom will be : -

A $4E_n$
B $\dfrac{E_n}{4}$
C $2E_n$
D $\dfrac{E_n}{2}$

The answer is A.

Solution

For a hydrogen-like atom: $E_n = -\dfrac{13.6Z^2}{n^2}$ eV, so $E \propto Z^2$ for the same n.
Hydrogen: Z = 1. Singly ionised helium ($He^+$): Z = 2.
$E_{He^+} = 2^2 \times E_n = 4E_n$

Concept Energy proportional to Z squared

Atoms in past papers

55 questions from this chapter have appeared across 25 exam years.