The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state (n) are respectively (Given : Hydrogen atom Bohr radius is 52.9 pm)

Formula

The Bohr radius for any hydrogen-like species is given by the formula:

• Radius of the state = Base Hydrogen radius × (n² / Z)

Where:

• Radius of the state = Bohr radius of the given species = 70.53 pm
• Base Hydrogen radius = Bohr radius of the hydrogen atom (first orbit) = 52.9 pm
• n = Principal quantum number (stationary state)
• Z = Atomic number of the species

Step-by-Step Calculation

Step 1: Find the ratio of n² to Z

• 70.53 = 52.9 × (n² / Z)
• n² / Z = 70.53 / 52.9
• n² / Z ≈ 1.333 (which equals the fraction 4 / 3)

Step 2: Test the options to find which pair gives a ratio of 4 / 3

• Option A: Li²⁺, 3
  • For Lithium (Li), Z = 3. Stationary state, n = 3.
  • Ratio: n² / Z = 3² / 3 = 9 / 3 = 3 (Incorrect)
• Option B: He⁺, 3
  • For Helium (He), Z = 2. Stationary state, n = 3.
  • Ratio: n² / Z = 3² / 2 = 9 / 2 = 4.5 (Incorrect)
• Option C: He⁺, 2
  • For Helium (He), Z = 2. Stationary state, n = 2.
  • Ratio: n² / Z = 2² / 2 = 4 / 2 = 2 (Incorrect)
• Option D: Li²⁺, 2
  • For Lithium (Li), Z = 3. Stationary state, n = 2.
  • Ratio: n² / Z = 2² / 3 = 4 / 3 (Correct!)