Answer
(a) increase
(b) $2cm$
Work Step by Step
(a) We know that $r=\frac{mv}{qB}$. This equation shows that if the speed of the isotopes is doubled then the separation $d$ increases.
(b) We can determine the required separation between the isotopes as follows:
$r_{235}=\frac{mv}{qB}$
$\implies r_{235}=\frac{(3.90\times 10^{-25}Kg)\times 2\times 1.05\times 10^5m/s}{(1.6\times 10^{-19}C)(0.750T)}$
$r_{235}=68.25cm$
and $r_{238}=\frac{mv}{qB}$
We plug in the known values to obtain:
$r_{238}=\frac{3.95\times 10^{-25}Kg\times 2\times 1.05\times 10^5m/s}{1.60\times 10^{-19}C\times 0.750T}$
$\implies r_{238}=69.125cm$
Now the separation is $d=2r_{238}-2r_{235}$
$d=2(69.125cm-68.25cm)$
$\implies d=1.75cm\approx 2cm$
