Doubly ionized helium ions are projected with a speed of 10 km s^...

The time period of a charged particle moving in a circular path in a uniform magnetic field is independent of its speed and is given by:

$T = \dfrac{2\pi m}{qB}$

For a doubly ionized helium ion (alpha particle):

Mass, $m \approx 4 \times 1.67 \times 10^{-27} \text{ kg}$

Charge, $q = 2e = 2 \times 1.6 \times 10^{-19} \text{ C}$

Substituting the given values $B = 1.0 \text{ T}$ and $\pi = 3.14$:

$T = \dfrac{2 \times 3.14 \times 4 \times 1.67 \times 10^{-27}}{2 \times 1.6 \times 10^{-19} \times 1.0}$

$T = \dfrac{3.14 \times 4 \times 1.67}{1.6} \times 10^{-8} \text{ s}$

$T \approx 1.31 \times 10^{-7} \text{ s}$