GREPhysics.NET: GR9277 #60

GR9277 #60

Problem

GREPhysics.NET Official Solution

\prob{60}
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

930rad/s
8.5E6rad/s
2.8E11rad/s
1.8E12rad/s
7.7E20rad/s

Electromagnetism $\Rightarrow$ }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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Comments

pgre
2013-10-15 21:20:06

Shouldn't cyclotron frequency be

$\frac{bq}{2 \pi m}$ ?

hipparcos
2018-04-05 15:24:41

The problem is asking for angular frequency.

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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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Shouldn't cyclotron frequency be $\frac{bq}{2 \pi m}$ ?

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