Radius of the first excited state of Helium ion is given as: a0 =… — Solution | JEE Chemistry

MCQEasyJEE 2025Bohr Model & Hydrogen Spectrum

Radius of the first excited state of Helium ion is given as: $a_0$ = radius of first stationary state of hydrogen atom.

A
$r = \frac{a_0}{2}$
B
$r = \frac{a_0}{4}$
C
$r = 4a_0$
D
$r = 2a_0$

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Helium ion is $He^+$ and the question asks for the radius of the first excited state. Also, $a_0$ is the radius of the first stationary state of the hydrogen atom.

Find: Radius of the first excited state of $He^+$ .

For a hydrogen-like ion, the radius of the ** $n$ **th orbit is

r_n = a_0 \frac{n^2}{Z}

where $n$ is the principal quantum number and $Z$ is the atomic number.

For the helium ion $He^+$ , we have $Z = 2$ . The first excited state means $n = 2$ .

Substituting these values,

r_2 = a_0 \frac{2^2}{2} = a_0 \frac{4}{2} = 2a_0

Therefore, the radius of the first excited state of helium ion is $2a_0$ . The correct option is D.

Common mistakes

Using $n = 1$ instead of $n = 2$ . This is wrong because the first excited state corresponds to $n = 2$ , not the ground state. Always identify the correct energy level before substitution.
Forgetting that $He^+$ is a hydrogen-like ion with $Z = 2$ . This gives an incorrect radius because the nuclear charge must appear in the denominator. Always use the atomic number of the ion.
Using the formula without the $Z$ factor, as if the species were hydrogen. That is incorrect because helium ion has a stronger nuclear attraction than hydrogen. Use $r_n = \frac{n^2 a_0}{Z}$ for hydrogen-like ions.

Practice more Bohr Model & Hydrogen Spectrum questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on Bohr Model & Hydrogen Spectrum

Answer

Step-by-step solution

Common mistakes

Practice more Bohr Model & Hydrogen Spectrum questions

Related questions