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Atoms and Nuclei question

2022 · 25 Jul · Shift 1 · Q59
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  5. /2022 · 25 Jul · Shift 1 · Q59

Atoms and Nuclei question

2022 · 25 Jul · Shift 1 · Q59

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :
  1. A
    μ⃗L=eL→2 m\vec{\mu}_{\mathrm{L}}=\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}μ​L​=2 meL​
  2. B
    μ⃗L=−eL→2 m\vec{\mu}_{\mathrm{L}}=-\frac{\overrightarrow{\mathrm{eL}}}{2 \mathrm{~m}}μ​L​=−2 meL​
  3. C
    μ⃗l=−eL→ m\vec{\mu}_{l}=-\frac{\overrightarrow{e L}}{\mathrm{~m}}μ​l​=− meL​
  4. D
    μ⃗l=2eL→m\vec{\mu}_{l}=\frac{2 \overrightarrow{\mathrm{eL}}}{\mathrm{m}}μ​l​=m2eL​
View written solutionFree

Correct answer: B

  1. Magnetic moment of a revolving charge

    For a particle of charge qqq moving in a circular orbit, the orbital magnetic moment is related to its orbital angular momentum L⃗\vec LL by

    μ⃗=q2m L⃗\vec \mu = \frac{q}{2m}\,\vec Lμ​=2mq​L

    where mmm is the mass of the particle.

  2. Apply for an electron

    An electron has charge

    q=−eq = -eq=−e

    where e>0e>0e>0 is the magnitude of electronic charge.

    Therefore,

    μ⃗L=−e2m L⃗\vec \mu_L = \frac{-e}{2m}\,\vec Lμ​L​=2m−e​L

    or

    μ⃗L=−eL⃗2m\boxed{\vec \mu_L = -\frac{e\vec L}{2m}}μ​L​=−2meL​​

  3. Physical meaning of the negative sign

    The negative sign shows that the magnetic moment vector of the electron is opposite to its orbital angular momentum vector, because the electron is negatively charged.

  4. Check the options

    • A: μ⃗L=eL⃗2m\vec{\mu}_L=\dfrac{e\vec L}{2m}μ​L​=2meL​ → wrong sign
    • B: μ⃗L=−eL⃗2m\vec{\mu}_L=-\dfrac{e\vec L}{2m}μ​L​=−2meL​ → correct
    • C: μ⃗l=−eL⃗m\vec{\mu}_l=-\dfrac{e\vec L}{m}μ​l​=−meL​ → wrong factor
    • D: μ⃗l=2eL⃗m\vec{\mu}_l=\dfrac{2e\vec L}{m}μ​l​=m2eL​ → wrong sign and wrong factor

  5. Final answer

    The correct expression is

    μ⃗L=−eL⃗2m\boxed{\vec{\mu}_L=-\frac{e\vec L}{2m}}μ​L​=−2meL​​

    so the correct option is B.

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