Question

An oxygen-16 ion with a mass of perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius.

Required:
a. 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.

Answer 1

a) 4.8*10^-19 C

b) 3

Step-by-step explanation:

We know that

F = ma

Also, recall that a = v²/r and F = qvB

Substituting this in the first equation, we have

qvB = mv²/r, since we're looking for q, we make it the subject of the formula and solve for it.

q = mv²/rvB

q = mv/rB

q = [2.66*10^-26 * (5*10^6)] / 0.231 * 1.2

q = 1.33*10^-19 / 0.2772

q = 4.8*10^-19 C

Ratio between the charge and the electron is q/c =

4.8*10^-19 / 1.6*10^-19 = 3

Therefore, the ratio between the charge and electron is 3