Ions having equal charges but masses of M and 2 M are accelerated through the sa

Question

Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter? Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

Explanation / Answer

workdone = 0.5*2M*v^2 = 0.5*M*V'^2

==> V' = V*sqrt(2)

we know
r = m*v/B*q



R/R' = 2M*V/M*v'

R/R' = 2M*v / (M*V*sqrt(2)

R/R' = 2/sqrt(2)

R' = R*sqrt(2)/2 = 0.707*R

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