JEE Main202522 Jan 2025Morning ShiftPhysicsDual Nature of MatterActual
An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 10⁻¹¹ ~m while that for the electron in third excited state is 8.48 10⁻¹⁰ ~m . The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is
Options
- A3
- B16
- C9
- D4
Correct answer
D. 4
Step-by-step solution
= h mv aligned & mvr = nh 2 & mv = nh 2 r & = 2 rh nh & r n & ₁ ₄ = r ₁ n ₄ n ₁ r ₄ = 5.3 10⁻¹¹ 4 1 84.8 10⁻¹¹ & ₁ ₄ = 1 4 aligned