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?

\frac{R}{^{\sqrt{2}}}

Explanation:

q1 = q , q2 = q

m1 = M, m2 = 2M

Potential difference is V

Let v1 be the speed of first particle and v2 be the speed of second particle.

Energy due to potential difference gives the kinetic energy to the particle.

1/2 m x v^2 = e V

v^2 = 2 e V / m = 2e V / m ... (1)

Now radius is given by

r = m v / B q

by eqution (1)

For first particle

  .... (2)

For second particle

   .... (3)

Divide equation (2) by equation (3), we get

So

r1 / r2 =