Answer
2.5 m.
Work Step by Step
The charged particles in the mass spectrometer trace a semicircular path (Figure 20–41). The desired separation of the molecules, on the film, is 0.50 mm.
The distance between where a particle enters, and where it strikes the film, is 2r. So, the difference in path radii for the two molecules is 0.25 mm.
$$qvB=ma=m\frac{v^2}{r}$$
Note that q, B, and v are the same, so the ratio m/r is the same for the two molecules.
$$\frac{m}{r}=\frac{qB}{v}$$
$$\frac{m_{CO}}{r_{CO}}=\frac{m_{N_2}}{r_{N_2}}$$
$$\frac{28.0106u}{r}=\frac{28.0134}{r+2.5\times10^{-4}m}$$
$$r=2.5m$$