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Question

# $(a)$ 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

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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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