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JEE Main 201511 AprilOnline
Exam
JEE Main
Year
2015
Date
11 April
Mode
Online
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2015 · 11 April · Online · Physics · Dual Nature of Matter

The de-Broglie wavelength associated with the electron in the n = 4...

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

Options

  1. AHalf of the de-Broglie wavelength of the electron in the ground state
  2. BFour times the de-Broglie wavelength of the electron in the ground state
  3. C14th\dfrac{1}{4}th of the de-Broglie wavelength of the electron in the ground state
  4. 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=hp\lambda = \dfrac{h}{p}

∵p22m=k⇒p=2mk∵ \dfrac{{p}^{2}}{2m} = k ⇒ p = \sqrt{2mk}

⇒λ=h2mk⇒ \lambda = \dfrac{h}{\sqrt{2mk}}

At ground level energy =E0= {E}_{0} so

At n=4n = 4 level energy =E0n2=E016= \dfrac{{E}_{0}}{{n}^{2}} = \dfrac{{E}_{0}}{16}

∴∴ at ground level

λ0=h2mE0{\lambda}_{0} = \dfrac{h}{\sqrt{2m{E}_{0}}}

At n = 4 level

λ′=h2mE016=4h2mE0{\lambda}^{′} = \dfrac{h}{\sqrt{2m\dfrac{{E}_{0}}{16}}} = \dfrac{4h}{\sqrt{2m{E}_{0}}}

⇒λ′=4λ0⇒ {\lambda}^{′} = 4{\lambda}_{0}
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