Application of mass spectrometry: relative isotopic mass

A mass spectrometer measures the mass of an isotope relative to that of carbon-12 by analysing the ratio of the ionised isotope’s deflection to the ionised carbon-12’s deflection.

From eq9, we have:

\frac{e_{isotope}}{m_{isotope}}=\frac{E\theta _{isotope}}{B^{2}L}\; \; \; \; \; \; \; (10)

\frac{e_{^{12}C}}{m_{^{12}C}}=\frac{E\theta _{^{12}C}}{B^{2}L}\; \; \; \; \; \; \; (11)

Assume both ions are univalent so that e_{^{12}C}=e_{isotope} and divide eq11 by eq10:

\frac{m_{isotope}}{m_{^{12}C}}=\frac{\theta _{^{12}C}}{\theta _{isotope}}\; \; \; \; \; \; \; (12)


mass\; of\; isotope=\frac{\theta _{^{12}C}}{\theta _{isotope}}m_{^{12}C}\; \; \; \; \; \; \; (13)

We can also represent eq13 in the form

mass\; of\; isotope=\frac{m_{isotope}/z_{isotope}}{m_{^{12}C}/z_{^{12}C}}m_{^{12}C}\; \; \; \; \; \; \; (14)

where we have replaced e with the notation z. The output of eq14 is a value with unit of unified atomic mass unit, u, since the ratio is unit-less while m_{^{12}C}=12u.

Finally, we divide the output of eq14 by 1u to obtain the relative isotopic mass, which is a dimensionless quantity that is defined as the ratio of the mass of an isotope in unified atomic mass unit to one unified atomic mass unit.



Is it possible to accurately measure the mass of an atom in kg using eq9 without a reference isotope?


No. Due to the limits of precision engineering, measurements of the mass of an atom in kg by directly applying eq9 differ from one mass spectrometer to another. We therefore need a reference ‘flight path’ that we can compare with, i.e. using eq14. Since the value of m_{^{12}C} is accurately defined in u, the output of eq19 must be in unified atomic mass unit. The value in kg is then obtained by the following conversion:

1u = 1.660539 x 10-27 kg


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