Question

The cyclotron frequency of an electrons gyrating in a magnetic field of $1$T is approximately

• A. $28MHz$
• B. $280MHz$
• C. $2.8MHz$
• D. $28GHz$

Answer 1

The correct option is D $28GHz$

For an electron gyrating in a magnetic field $\frac{m{v}^2}{r}=Bqv$

$r=\frac{mv}{Bq}\Rightarrow \frac{v}{r}=\frac{Bq}{m}$

$T=\frac{2\pi r}{v};n=\frac{1}{T}=\frac{v}{2\pi r}=\frac{Bq}{2\pi m}$

$n=\frac{1\times 1.6\times {10}^{-19}}{2\times \pi \times 9.1\times {10}^{-31}}$

$=\frac{1.6\times {10}^{12}}{2\pi \times 9.1}=28$GHz