A mass spectrometer is designed to separate atoms of carbon to determine the fra

Question

A mass spectrometer is designed to separate atoms of carbon to determine the fraction of different isotopes. (Isotopes of an element, as we will see in chapter 20, have the same atomic number but different atomic mass, due to different numbers of neutrons.) There are three main isotopes of carbon, with the following atomic masses:

12C                 1.99x10-26kg

13C                 2.16x10-26kg

14C                 2.33x10-26kg

The atoms of carbon are singly ionized and enter a mass spectrometer with magnetic field strength B=0.200T at a speed of 1.50x105m/s. The ions move along a semicircular path and exit through an exit slit. How far from the entrance will the beams of the different isotope ions end up?

Explanation / Answer

When these ions enter a region of uniform magnetic field, the field bends the ions into circular trajectories; the radius of circular trajectory is given by the formula

     r = mv/Bq

here m is mass of the isotope

the mass of 12C = 1.99*10^-26 kg

the radius of the cirular path

        r12 = (1.99*10^-26 kg) (1.5*10^5) / (0.2T)(1.6*10^-19C)

              = 0.0009328125 = 9.33*10^-4 m

the mass of 13C = 2.16*10^-26 kg

the radius of the cirular path

        r12 = (2.16*10^-26 kg) (1.5*10^5) / (0.2T)(1.6*10^-19C)

              = 0.10125 =101.25 *10^-3 m

the mass of 14C = 2.33*10^-26 kg

the radius of the cirular path

        r12 = (2.33*10^-26 kg) (1.5*10^5) / (0.2T)(1.6*10^-19C)

              = 0.1092 =109.2 *10^-3 m

Therefore the isotopes ions are ends up at distance from the entrance

at 9.33*10^-4 m , 101.25 *10^-3 m and 109.2 *10^-3 m

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