Question

# (a) An oxygen-16 ion with a mass of $2.66 \times 10^{-26} \mathrm{kg}$ travels at $5.00 \times 10^{6} \mathrm{m} / \mathrm{s}$ perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.

Solution

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$\textit{\textbf{Strategy}}$:

$\textbf{Part (a):}$

To get the charge of the oxygen-16 ion, we will use the equation $r = \frac{mv}{qB}$ and solve it for $q$ where $m$ is the ion's mass.

\begin{align*} q = \frac{mv}{rB} = \frac{2.66 \times 10^{-26} \text{ kg} \times 5 \times 10^{6} \text{ m/s}}{0.231 \text{ m} \times 1.2 \text{ T}} = 4.8 \times 10^{-19} \text{ C} \end{align*}

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