Cyclotron Resonance: Lower Limit for Electron Scattering Time

[Matt atkinson]

Homework Statement

Calculate the lower limit of the electron scattering time in a material placed in a magnetic field of 1 T which is necessary to observe cyclotron resonance. The electron effective mass in the material
is 0.06 $m_o$ (where $m_o$ is the free electron mass).

Homework Equations

$\omega_c=\frac{eB}{0.06m_o}$
$\tau_{min}=\frac{2\pi}{\omega_c}$

The Attempt at a Solution

So I basically substituted values into $\omega_c$ and then into the equation for $\tau_c$ i got $\tau_c=2.14ps$ whereas the answer says $\tau_c=0.54ps$, have I gone wrong? or is the solution given wrong, because i have done it multiple times.

 

[mfb]

The two answers differ by a factor of 4 (+-2%). I guess they took 1/4 of a cycle to be sufficient (some electrons won't scatter for 4 times the scattering time). There is no absolute limit, a shorter time just makes observations harder.

 

[Matt atkinson]

ah okay! Thankyou very much I did notice the factor of 4 difference just wasn't sure where it came from.