Question

The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li²⁺ ion (atomic number = 3) in a similar state is ______.

Options

• 0.17 Å

• 0.265 Å

• 0.53 Å

• 1.06 Å

Answer 1

The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li²⁺ ion (atomic number = 3) in a similar state is 0.17 Å.

Explanation:

a₀ is the Bohr radius (radius of hydrogen in ground state) = 0.53 Å.

n is the principal quantum number (for ground state, n = 1).

Z is the atomic number of the element.

The atomic number Z = 3.

The ground state means n = 1.

Use the Bohr formula for hydrogen‑like ions:

`r_n = (a_0 xx n^2)/Z`

`r = (0.53 xx (1)^2)/3`

`r = 0.53/3`

r ≈ 0.1766 Å