A mass spectrometer is being used to monitor air pollutants. it is difficult, however, to separate molecules with nearly equal mass such as Co (28.0106 u) and N2 (28.0134 u).
How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.25 mm ?

The answer is 1250 mm

Explanation:

The path that particles move in the spectrometer is semicircular. Each of the particles has a displacement of twice the radius (2r) from the entrance to where the film is hit. According to the exercise, if the separation between the two molecules is 0.25 mm, then the difference in the radius of the molecules is equal to 0.125 mm. The ratio of mass/radius is equal for molecules, and therefore is equal to:

m = q * B * r / v

m/r = constant

(m/r)CO = (m/r)N = (28.0106 u/r) = (28.0134 u/(r + 0.000125 m))

Clearing and solving r:

r = 1.25 m = 1250 mm

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