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NEET Physics QUESTION #1033
Question 1
A model states flux through electron orbit in magnetic field \(B\) is \(n(h/e)\). The magnetic moment in the lowest energy state (\(n=1\)) is:
  • \(\dfrac{heB}{\pi m}\)
  • \(\dfrac{heB}{2\pi m}\)✔️
  • \(\dfrac{he}{\pi m}\)
  • \(\dfrac{he}{2\pi m}\)
Correct Answer Explanation
Flux: \(B\pi r^2 = \frac{nh}{e}\Rightarrow r^2 = \frac{nh}{\pi eB}\). For \(n=1\): \(r=\sqrt{\frac{h}{\pi eB}}\). \(mv^2/r = evB\Rightarrow v = \frac{eBr}{m}\). Magnetic moment \(\mu = iA = \frac{ev}{2\pi r}\cdot\pi r^2 = \frac{evr}{2} = \frac{e}{2}\cdot\frac{eBr^2}{m} = \frac{e^2Bh}{2\pi em} = \frac{heB}{2\pi m}\).