Question

The ratio of the areas within the electron orbits for the first excited state to the ground state for the hydrogen atom is –

• A. 2 : 1
• B. 4 : 1
• C. 8 : 1
• D. 16 : 1

Answer 1

Answer: (D)

16 : 1

Answer 2

First excited state implies n = 2, while ground state implies n = 1. If radius of orbit in ground state, r₁ = a₀, then radius of orbit in first excited state = r₂ = n²r₁ = (2)²r₁ = 4r₁ = 4a₀

\ A₁ = p$r_{1}^{2}$ = p$a_{0}^{2}$

and A₂ =$\pi r_{2}^{2}$= p(4a₀)² = 16$\pi a_{0}^{2}$

Hence, (A₂/A₁) = (16/1)