Question

If the radius of ground state hydrogen is 51 pm, find out the radius of 5th orbit of Li²⁺ ions. (closest integer)

Answer 1

Correct Answer: 425

The radius of an electron orbit in a hydrogen-like atom is given by the formula:
r_n = r₁ × n² × Z^-1,
where:

• r₁ is the radius of the ground state (n=1) of hydrogen,
• n is the principal quantum number (orbit number),
• Z is the atomic number of the ion.

Given: r₁ = 51 pm for hydrogen, atomic number Z = 3 for Li²⁺, and n = 5 for the 5th orbit.
Using the formula, the radius of the 5th orbit of Li²⁺ is:
r₅ = 51 pm × 5² × 3^-1
Calculate:
r₅ = 51 pm × 25 × (1/3)
r₅ = (51 × 25) / 3 pm
r₅ = 1275 / 3 pm
r₅ = 425 pm.
The computed radius of the 5th orbit of Li²⁺ is 425 pm, which fits within the expected range of 425 to 425 pm.