Question

Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.547 T.

Answer 1

Answer:

Wavelength is 0.359 m

Explanation:

Given that,

Magnetic field, B = 0.547 T

We need to find the wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.547 T.

The frequency of revolution of proton in the cyclotron is given by :

$f=\dfrac{qB}{2\pi m}$

m is mass of proton

q is charge on proton

So,

$f=\dfrac{1.6\times 10^{-19}\times 0.547}{2\pi \times 1.67\times 10^{-27}}\\\\f=8.34\times 10^6\ Hz$

We know that,

Speed of light, $c=f\lambda$

$\lambda$ = wavelength

$\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{834\times 10^6}\\\\\lambda=0.359\ m$

So, the wavelength of the radiation produced by a proton is 0.359 m.