The de-Broglie wavelength associated with the electron in the n = 4 level is:

The de-Broglie wavelength associated with the electron in the n=4 level is:

  1. Half of the de-Broglie wavelength of the electron in the ground state
  2. Four times the de-Broglie wavelength of the electron in the ground state
  3. 14th of the de-Broglie wavelength of the electron in the ground state
  4. Two times the de-Broglie wavelength of the electron in the ground state

Solution

De-Broglie wavelength is given as

λ=hp

∵p22m=k⇒p=2mk

⇒λ=h2mk

At ground level energy =E0 so

At n=4 level energy =E0n2=E016

∴ at ground level

λ0=h2m E0

At n = 4 level

λ′=h2mE016=4h2m E0

⇒λ′=4λ0

Asked in: JEE Main 2015 (11 Apr Online)

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