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

Wavelength is 0.359 m

Step-by-step 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=(qB)/(2\pi m)`

m is mass of proton

q is charge on proton

So,

`f=(1.6* 10^(-19)* 0.547)/(2\pi * 1.67* 10^(-27))\\\\f=8.34* 10^6\ Hz`

We know that,

Speed of light,
`c=f\lambda`

`\lambda` = wavelength

`\lambda=(c)/(f)\\\\\lambda=(3* 10^8)/(834* 10^6)\\\\\lambda=0.359\ m`

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