If the radius of the 3ʳᵈ Bohr's orbit of hydrogen atom is r₃ and the radius of 4ᵗʰ Bohr's orbit is r₄. Then :

Solution

Chemistry ma’am · 3 steps

Bohr radius grows as the square of n, so square both orbit numbers before you take the ratio.

1. Radius formula. For a hydrogen-like atom the Bohr radius depends on n²/Z. For hydrogen Z = 1, so the radius is directly proportional to n².

   rₙ = 0.529 Å × n²/Z

2. Take the ratio. Dividing the two radii cancels the constant and Z: r₄/r₃ = 4²/3² = 16/9.
3. So. r₄ = 16/9 r₃, which is option (b). The outer orbit is larger, as it must be.

The idea to keep. In Bohr's model radius goes as n², velocity as 1/n and energy as -1/n². Always check which power of n a quantity carries before writing a ratio.

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