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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Physics
Chapter
Atomic Physics

JEE Main 2017 · 8 April · Online · Physics · Atomic Physics

According to Bohr's theory, the time averaged magnetic field at the...

According to Bohr's theory, the time averaged magnetic field at the centre (i.e., nucleus) of a hydrogen atom due to the motion of electrons in the nth{n}^{th} orbit is proportional to: (n=n = principal quantum number)

Options

  1. An−3{n}^{- 3}
  2. Bn−2{n}^{- 2}
  3. Cn−4{n}^{- 4}
  4. Dn−5{n}^{- 5}

Correct answer

D. n−5{n}^{- 5}

Step-by-step solution

v∝znv ∝ \dfrac{z}{n}

r∝n2zr ∝ \dfrac{{n}^{2}}{z}

B=\muI2RB = \dfrac{\muI}{2R}

I=eT=e(2\piRv)=e2πvRI = \dfrac{e}{T} = \dfrac{e}{( \dfrac{2\piR}{v} )} = \dfrac{e}{2\pi} \dfrac{v}{R}

B=μ02e2πvR2B = \dfrac{{\mu}_{0}}{2} \dfrac{e}{2\pi} \dfrac{v}{{R}^{2}}

B=μ0e4πzn(n2z)2B = \dfrac{{\mu}_{0} e}{4\pi} \dfrac{z}{n{( \dfrac{{n}^{2}}{z} )}^{2}}

B=μ0e4πz3n5B = \dfrac{{\mu}_{0}e}{4\pi}\dfrac{{z}^{3}}{{n}^{5}}

B∝n−5B ∝ {n}^{- 5}.
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