Answer :
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 :
[tex]f=\dfrac{qB}{2\pi m}[/tex]
m is mass of proton
q is charge on proton
So,
[tex]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[/tex]
We know that,
Speed of light, [tex]c=f\lambda[/tex]
[tex]\lambda[/tex] = wavelength
[tex]\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{834\times 10^6}\\\\\lambda=0.359\ m[/tex]
So, the wavelength of the radiation produced by a proton is 0.359 m.