Radius of a certain orbit of hydrogen atom is 8.48 Aᵒ. If energy of electron in this orbit is E / x. then x= ________ (Given a₀=0.529 Aᵒ, E= energy of electron in ground state).

Solution

Physics sir · 4 steps

Radius grows as n² and energy falls as 1/n², so the same ratio n² answers both.

1. Radius gives n. In Bohr's model the radius of the nth orbit of hydrogen is rₙ = n² a₀. Divide the given radius by a₀ to get n².

   n² = rₙ/a₀ = (8.48 Å)/(0.529 Å) ≈ 16

2. Find the orbit. n² = 16, so n = 4. Check: 16 × 0.529 = 8.464 ≈ 8.48.
3. Energy in that orbit. For hydrogen Eₙ = E/n², where E is the ground-state energy. With n = 4, E₄ = E/16.
4. So. Comparing with E/x gives x = 16.

The common slip: 4. Stopping at the orbit number gives 4, not 16. Energy depends on n², so it must be squared.

The idea to keep. In hydrogen, rₙ ∝ n² and Eₙ ∝ 1/n². So rₙ/a₀ is exactly the factor by which the energy is divided. You do not even need to find n separately.

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