S.A. Goudsmit devised a method for measuring accurately the masses of heavy ions by timing their period of revolution in a known magnetic field. A singly charged ion of iodine makes 7.00 rev in a field of 45.0 mT in 1.29 ms. We have to calculate its mass, in atomic mass units. Actually, the mass measurements are carried out to much greater accuracy than these approximate data suggest.

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Let R be the radius of the circular orbit of charged iodine ion in a uniform magnetic field, B, perpendicular to its velocity, v. Equation of motion for the circular motion of the charged ion is

Number of revolutions that an ion would make per second will, therefore, be

Data of the problem are:

As

mass of the iodine ion in atomic mass units will be

The precisely measured value of the mass of an iodine atom is 126.948 u.

With the developments in the mass-spectrometry, the mass measurements are carried out to much greater accuracy than what the approximate data of Goudsmit suggests.