Physicist S. A. Goudsmit devised a method for measuring the mass of heavy ions by timing their period of revolution in a known magnetic field. A singly charged ion makes 5.00 revolutions in a 50.0 mT field in 1.11 ms. Calculate its mass, in atomic mass units.

170.36 amu

Explanation:

Ion makes 5 revolutions in 1.11 ms

Frequency = 5 / (1.11 x 10^-3) = 4504.5 rps

B = 50 mT = 0.05 T

q = 1.6 x 10^-19 C

Let m be the mass in kg

Time period is given by

T = (2 π m) / (B q)

Frequency is the reciprocal of time period.

f = 1 / T = B q / 2πm

So,

m = B q / 2 π f

m = (0.05 x 1.6 x 10^-19) / (2 x 3.14 x 4504.5) = 2.828 x 10^-25 kg

as we know that

1 amu = 1.66 x 10^-27 kg

So, m = (2.828 x 10^-25) / (1.66 x 10^-27) = 170.36 amu