An electron, a proton and an alpha particleÂ having the same kinetic energy are moving in circular o

Question

An electron, a proton and an alpha particleÂ having the same kinetic energy are moving in circular orbits of radii re, rp, rÎ±Â respectively in a uniform magnetic field B. The relation between re, rp, rÎ±Â is:-

Accepted Answer

Radius of circular path in magnetic field is given
by R =Â $\frac{\sqrt{3 Â K m}}{q B}$
where K = kinetic energy of particle
m = mass of particle
q = charge on particle
B = magnetic field intensity
R = radius of path
For electron
$r_{e} = \frac{\sqrt{2 Â K Â m_{e}}}{eB}$ Â Â ...(i)
For proton
$r_{p} = \frac{\sqrt{2 Â K Â m_{p}}}{eB}$ Â Â ...(ii)
For $Î±$ particle
$r_{Î±} = \frac{\sqrt{2 K m_{Î±}}}{q_{Î±} B} = \frac{\sqrt{2 K Â 4 m_{p}}}{2 e B} = \frac{\sqrt{2 K m_{p}}}{e B}$ Â ...(iii)
as me < m_p so r_e < r_p = r_$Î±$

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