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Isotope Separation

The differential abundance of isotopes allows for separation of ions based on their mass, often used in techniques like GC-MS.
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The statement of the theorem

Let m1m_1 and m2m_2 be the masses of two isotopes, and qq be the charge. The separation factor α\alpha for the mass-to-charge ratio m/zm/z is defined by the ratio of the measured ion intensities II: \nα=I(m1/q)I(m2/q)≈m1m2\alpha = \frac{I(m_1/q)}{I(m_2/q)} \approx \frac{m_1}{m_2} \nFor high-resolution separation, the differential abundance ΔA\Delta A of an isotope mim_i relative to a reference isotope mrefm_{ref} is modeled by the ratio of their natural abundances AiA_i: \nAiAref=NiNref≈mimref⋅e−(mi−mref)22σ2\frac{A_i}{A_{ref}} = \frac{N_i}{N_{ref}} \approx \frac{m_i}{m_{ref}} \cdot e^{-\frac{(m_i - m_{ref})^2}{2\sigma^2}} \nwhere σ\sigma is the mass resolution parameter.
Source: Wikipedia