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 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: The atoms of carbon are singly ionized and enter a mass spectrometer with magnetic field strength B = 0.200 T at a speed of 1.5 times 10^5 m/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? A mass spectrometer is designed to separate atoms of carbon to determine the fraction of different isotopes. (Isotopes of an element 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: The atoms of carbon are singly ionized and enter a mass spectrometer with magnetic field strength B = 0.200 T at a speed of 1.5 times 10^5 m/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

Force, F=ma

Centripetal force, mv2/r=Bqv

r=mv2/Bqv

2r=2mv/Bq

Thus the distance between each isotope is,

(2r)1=(1.99*10-26)(2*1.5*105)/(1.6*10-19)*0.2=18.66 cm

(2r)2=(2.163*10-26)(2*1.5*105)/(1.6*10-19)*0.2=20.25 cm

(2r)3=(2.333*10-26)(2*1.5*105)/(1.6*10-19)*0.2=21.84 cm

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