Answer
The other isotope masses are 70 u, 72 u, 73 u, and 74 u.
Work Step by Step
Equation 20-12 for the mass spectrometer shows that the ion’s mass is proportional to the radius of the circular path that it follows.
$$m=r\frac{qB}{v}$$
We solve for the ratio of mass to radius for this situation, using data given in the problem for germanium.
$$\frac{m}{r}=\frac{qB}{v}=\frac{76\;u}{22.8\;cm}$$
Apply this to each of the “mystery” radii.
$$\frac{m_{21.0cm}}{21.0cm}=\frac{76\;u}{22.8\;cm}$$
$$ m_{21.0cm}=70\;u$$
$$\frac{m_{21.6cm}}{21.6cm}=\frac{76\;u}{22.8\;cm}$$
$$ m_{21.6cm}=72\;u$$
$$\frac{m_{21.9cm}}{21.9cm}=\frac{76\;u}{22.8\;cm}$$
$$ m_{21.9cm}=73\;u$$
$$\frac{m_{22.2cm}}{22.2cm}=\frac{76\;u}{22.8\;cm}$$
$$ m_{22.2cm}=74\;u$$
