Question

Chlorine is an unusual element in that it has two abundant stable isotopes, Cl-35 and Cl-37, constituting, respectively, about 76% and 24% of natural chlorine. The masses of these isotopes in unified atomic mass units, are, to three significant figures, equal to their mass numbers of 35 and 37. A mass spectrometer is used with singly ionized chlorine atoms. The spectrometer has a 3.5-kV accelerating potential and a 163-mT magnetic field. How far apart will Cl-35 and Cl-37 ions be when they reach the detector

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Answer 1

Let us consider the velocity of the charged particle (charge q and mass m) in an applied potential difference V, is v. Then the expression for velocity will be (kinetic energy will be equal to the potential energy due to the potential)

Now, due to the effect of magnetic field (B), the charged particle will move in a circular path of radius r. Here, the magnetic force will provide the centripetal force of the particle. Hence, you can write

In this figure, you can see that the charged particle will deflect a distance of 2r or D. Hence, in your problem you have to find the value of D for two cases.

An atomic mass unit is equal to 1.67 x 10^-27 Kg up to three significant digit. Therefore, the masses of two isotopes of chlorine will be

The potential difference V = 3.5 kV = 3500 V. For singly ionized chlorine atoms, the charge will be equal to 1.602 x ^-19 C or charge of an electron. Putting the values of masses, you can obtain the deflections as