Question

Find out 5^th orbit radius (in pm) of Li⁺⁺ if ground orbit radius of H-atom is 51 pm.

Answer 1

Correct Answer: 425

The radius of the orbit for a hydrogen-like atom is given by the formula: r_n = a₀n² Z^-1, where r_n is the radius of the n^th orbit, a₀ is the Bohr radius for the hydrogen atom, Z is the atomic number, and n is the principal quantum number. For hydrogen, a₀ is given as 51 pm. Since Li⁺⁺ resembles a hydrogen-like atom with Z = 3, we calculate:

Step 1: Identify Known Values

• a₀ = 51 pm
• Z = 3
• n = 5

Step 2: Calculate the Radius of the 5^th Orbit
Using the formula:
r₅ = 51 × (5)² × 3^-1
Calculate n²:
5² = 25
Substitute back:
r₅ = (51 × 25) / 3 = 425 pm

Step 3: Validate the Computed Radius against the Range

• The calculated radius of 425 pm fits exactly within the specified range of 425, 425.

Therefore, the radius of the 5^th orbit of Li⁺⁺ is 425 pm.