Final answer:
The positive charge on the oxygen-16 ion is 1.60 x 10^-19 C. The ratio of this charge to the charge of an electron is 1. This ratio is an integer because charge is quantized and comes in discrete multiples of the elementary charge.
Step-by-step explanation:
To find the positive charge on the oxygen-16 ion moving in a magnetic field, we need to use the formula for the magnetic force acting on a charged particle moving perpendicular to a magnetic field, which is F = qvB, where F is the force, q is the charge, v is the velocity, and B is the magnetic field strength. Since the ion is moving in a circle, the magnetic force will act as the centripetal force, which is F = mv2/r, where m is the mass and r is the radius of the circular path. Setting the centripetal force equal to the magnetic force, we get mv2/r = qvB.
Solving for q, gives us q = mv2/(rB). Plugging in the values, q = (2.66×10−26 kg)(5.00×106 m/s)2/(0.231 m)(1.20 T), which calculates to 1.60 x 10−19 C. Therefore, the positive charge on the ion is 1.60 x 10−19 C.
(b) The charge of an electron is −1.60 x 10−19 C. The ratio of the ion's charge to that of an electron is 1.60 x 10−19 C / 1.60 x 10−19 C = 1.
(c) The ratio should be an integer because charge is quantized, meaning it comes in discrete multiples of the elementary charge, which is the charge of a single proton (or the negative of that for an electron).