Explanation:
Let [tex]m_p[/tex] is the mass of proton. It is moving in a circular path perpendicular to a magnetic field of magnitude B.
The magnetic force is balanced by the centripetal force acting on the proton as :
[tex]\dfrac{mv^2}{r}=qvB[/tex]
r is the radius of path,
[tex]r=\dfrac{mv}{qB}[/tex]
Time period is given by :
[tex]T=\dfrac{2\pi r}{v}[/tex]
[tex]T=\dfrac{2\pi m_p}{qB}[/tex]
Frequency of proton is given by :
[tex]f=\dfrac{1}{T}=\dfrac{qB}{2\pi m_p}[/tex]
The wavelength of radiation is given by :
[tex]\lambda=\dfrac{c}{f}[/tex]
[tex]\lambda=\dfrac{2\pi m_pc}{qB}[/tex]
So, the wavelength of radiation produced by a proton is [tex]\dfrac{2\pi m_pc}{qB}[/tex]. Hence, this is the required solution.
