## Related questions with answers

$(a)$ An oxygen-$16$ ion with a mass of $2.66 \times 10^{-26} \mathrm{~kg}$ travels at $5.0 \times 10^6 \mathrm{~m} / \mathrm{s}$ perpendicular to a $1.20 \mathrm{~T}$ magnetic field, which makes it move in a circular arc with a $0.231 \mathrm{~m}$ 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

Verified**a)** We're given the mass and the speed of an oxygen ion:

$m=2.66\cdot10^{-26}\,\text{kg}\\ v=5.0\cdot10^6\,\text{m/s}$

and the movement is perpendicular to the magnetic field:

$B=1.20\,\text{T}$

If the ion moves in a circular path with the radius:

$r=0.231\,\text{m}$

we need to calculate the charge of the ion (assuming it is positive).
**b)** We need to calculate the ratio of the charge calculated in the previous step and the one of an electron:

$|q_e|=1.602\cdot10^{-19}\,\text{C}$

**c)** We need to explain why the ratio calculated in the previous step should be an integer number.

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