JEE Main 2025 Apr 2 Shift 2, Physics Q11: Bohr Model of the Hydrogen Atom

JEE Main2025Apr 2, Shift 2Physics

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $Li^{++}$ ion in its ground state is given by $\frac{1}{X} a_{0}$ , where $X =$ ______. (Where $a_{0}$ is the first Bohr's radius.)

A
$2$
B
$1$
C
$3$
D
$9$

Solution

Bohr's expression for the orbital radius of a hydrogen-like ion is $r_{n} = a_{0} \frac{n ^{2}}{Z}$ .

For $Li^{++}$ , $Z = 3$ , and the ground state has $n = 1$ :

$r_{1} = a_{0} \cdot \frac{1 ^{2}}{3} = \frac{a _{0}}{3}$ .

Matching with $\frac{1}{X} a_{0}$ gives $X = 3$ .

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JEE Main 2025 Apr 2 Shift 2, Physics Q11: Bohr Model of the Hydrogen Atom

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