Please be as detailed as possible, I want to understand how to derive the answer
ID: 1445231 • Letter: P
Question
Please be as detailed as possible, I want to understand how to derive the answer.
In a cyclotron, the orbital radius of protons with energy 300 kcV is 17.0 cm. You are redesigning the cyclotron to be used instead for alpha particles with energy 300 kcV. An alpha particle has charge q = +2e and mass m = 6.64 times 10 27 kg. Part A If the magnetic field isnt changed, what will be the orbital radius of the alpha particles? Express your answer to three significant figures and include the appropriate unit)Explanation / Answer
The kinetic energies of both particles are equals, then
Kp = K
( mp Vp2 ) / 2 = ( m V2 ) / 2
mp Vp2 = m V2
where V = R
mp Rp2 p2 = m R2 2
since, the angular frequency of cyclotron is defined like
= ( q B ) / m
hence
mp Rp2 [ ( e B ) / mp ]2 = m R2 [ ( 2e B ) / m ]2
Rp2 / mp = ( 4 R2 ) / m
R = sqrt{ ( m Rp2 )/ ( 4 mp ) }
R = sqrt{ ( 6.64×1027 kg * ( 17.0 cm )2 )/ ( 4 * 1,67×1027 kg ) }
R = 16.9 cm