The radius of the 2nd orbit of Li²⁺ is x. The expected radius of the 3rd orbit of Be³⁺ is:

Radius of Orbits in Hydrogen-like Ions | JEE Main PYQ | Structure of Atom

Q. The radius of the 2^nd orbit of Li²⁺ is x. The expected radius of the 3^rd orbit of Be³⁺ is:

(A) 16/27 x

(B) 4/9 x

(D) 27/16 x

Correct Answer: 27/16 x

Explanation

For hydrogen-like species, radius of nth orbit is given by:

r_n ∝ n² / Z

For Li²⁺: Z = 3, n = 2

r = 2² / 3 = 4/3 (given as x)

For Be³⁺: Z = 4, n = 3

r = 3² / 4 = 9/4

Taking ratio:

(r_Be3+) / (r_Li2+) = (9/4) ÷ (4/3)

= (9/4) × (3/4) = 27/16

So required radius = 27/16 x

Previous Year Questions – Structure of Atom