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  GR9277 #60
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An electron in a metal has an effective mass $m^*=0.1m_e$. If this metal is placed in a magnetic field of magnitude 1 tesla, the cyclotron resonant frequency, $\omega_c$, is most nearly

  1. 930rad/s
  2. 8.5E6rad/s
  3. 2.8E11rad/s
  4. 1.8E12rad/s
  5. 7.7E20rad/s

Electromagnetism}Cyclotron Frequency

The cyclotron frequency is given by F=qvB = mv^2/r \Rightarrow qB=mv/r = m\omega, where one merely equates the Lorentz Force with the centripetal force using v=r\omega to relate angular velocity with velocity.

So, \omega = qB/m. Plug in the quantities to get choice (D).

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2013-10-15 21:20:06
Shouldn't cyclotron frequency be

\frac{bq}{2 \pi m} ?
2018-04-05 15:24:41
The problem is asking for angular frequency.
Kabuto Yakushi
2010-09-04 13:32:01
We have to be careful here, for m we can't use the mass of an electron: \m_e= \9\cdot10^{-31} or else we will get
\approx 10^{11} which is wrong. We have to use the effective mass supplied by by the question of m=.1\m_e.

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