JEE Main2015PhysicsDual Nature of MatterActual
The de-Broglie wavelength associated with the electron in the n = 4 level is:
Options
- AHalf of the de-Broglie wavelength of the electron in the ground state
- BFour times the de-Broglie wavelength of the electron in the ground state
- C1 4 t h of the de-Broglie wavelength of the electron in the ground state
- DTwo times the de-Broglie wavelength of the electron in the ground state
Correct answer
B. Four times the de-Broglie wavelength of the electron in the ground state
Step-by-step solution
De-Broglie wavelength is given as λ = h p ∵ p 2 2 m = k ⇒ p = 2 m k ⇒ λ = h 2 m k At ground level energy = E 0 so At n = 4 level energy = E 0 n 2 = E 0 16 ∴ at ground level λ 0 = h 2 m   E 0 At n = 4 level λ ′ = h 2 m E 0 16 = 4 h 2 m   E 0 ⇒ λ ′ = 4 λ 0