A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha pa

Question

A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference DeltaV. Each of the particles enters a uniform magnetic field Bvector, with its velocity in a direction perpendicular to Bvector. The proton moves in a circular path of radius rp. In terms of rp, determine the radius rd of the circular orbit for the deuteron. rd = 1 In terms of rp, determine the radius ralpha for the alpha particle. ralpha = 2

Explanation / Answer

rp=mpv/eB

(a) since v and B are the same

rd/rp = (2mp/mp)*(e/e)

rd=2rp

(b) since v and B are the same

r/rp = (4mp/mp)*(e/2e)

r=2rp

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