(a) An oxygen-16 ion with a mass of 2.66×10−26kg travels at 5.00×106m/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.

C) Yes it must be an integer because charges in nature are quantized in a unit of e, and so, atoms gain and lose charges in units of e. Thus, the charge on the oxygen atom must be multiple of e.

Explanation:

A) From Newton's second law, F = ma

Now, for a magnetic field we know that, F=qvB

Also, that a = v²/r

Thus putting v²/r for a in formula for force under Newton's second law, we have;

F = (mv²)/r

Thus, equating this with force formula from magnetic field to obtain ;

(mv²)/r = qvB

Making q the subject of the equation, we have,

q = (mv²)/(rvB) = mv/rB

Where m is the mass

q is the charge on ion

r is the radius

B is the magnetic field

v is the velocity

Thus,

q = [2.66×10^(−26) x 5 × 10^(6)]/(0.231 x 1.2) = 4.8 x 10^(-19) C

B) the ratio between the charge and that of an electron is; q/e

Now, charge on am electron has a value of 1.6 x 10^(-19) C

Thus,ratio is; [4.8 x 10^(-19)] / (1.6 x 10^(-19)) = 3

C) Yes it must be an integer because charges in nature are quantized in a unit of e, and so, atoms gain and lose charges in units of e. Thus, the charge on the oxygen atom must be multiple of e.