Assume that the radius of the first Bohr orbit of hydrogen atom is 0.6 Aᵒ . The radius of the third Bohr orbit of He⁺ is __________ picometer. (Nearest Integer)

Solution

Chemistry ma’am · 4 steps

Radius grows as n² and shrinks as Z, so scale the hydrogen value by n²/Z and convert to pm.

1. Bohr radius formula. For a one-electron species, the radius of the nth orbit is the first hydrogen orbit radius multiplied by n²/Z. He⁺ has only one electron, so this formula applies to it.

   rₙ = r₁ × n²/Z

2. Put in numbers. Here r₁ = 0.6 Å, n = 3 and Z = 2 for helium. So r₃ = 0.6 × 9/2 = 2.7 Å.
3. Convert to pm. 1 Å = 100 pm, so 2.7 Å = 270 pm.
4. So. The radius of the third Bohr orbit of He⁺ is 270 pm.

The common slip: 540. Leaving out Z = 2 treats He⁺ like hydrogen and gives 540, not 270.

The idea to keep. For any hydrogen-like ion, r ∝ n²/Z. A higher orbit pushes the electron out, and a bigger nuclear charge pulls it in.

Answer from the NTA final answer key. Solution by PrepWiser.