Answer
$t=5.07ns$
Work Step by Step
The time period of e- and e+ can be calculated from the formula:
$T=\frac{2{\pi}m}{qB}$
We plug in the known values to obtain:
$T=\frac{2(3.1416)(9.109\times 10^{-31})}{1.6\times 10^{-19}(3.53\times 10^{-3})}$
$T=10.133\times 10^{-9}$
$T=10.133ns$
We know that e- and e+ collide after $\frac{T}{2}$ so $t=\frac{T}{2}$ where $t$ is the time of collision between the two particles.
Now, we find $t$ by using the value of $T$ found above:
$t=\frac{10.133}{2}ns$
$t=5.07ns$
