How Do You Calculate Spatial Separation in a Mass Spectrometer?

[URIDON81]

Can anyone help with this problem, I have tried it a number of ways and can not get the correct answer, thanks in advance.

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 10-27 kg and 21.59 10-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 7.00 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.6600 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle.


I have been using the equation r=mv/eB but I think that I may be inputting the incorrect value for e since all the other variables are given.

 

[member 553083]

The answer is 0.711 m. The equation you are using is correct, but you need to make sure that you are using the appropriate value for e. In this case, it would be the charge of a single proton (1.6022 10-19C). Using this value, we can calculate the radius (r) for each isotope: r_12 = (19.93 10-27kg)(7.00 105m/s)/(1.6022 10-19C)(0.6600T) = 0.711 m r_13 = (21.59 10-27kg)(7.00 105m/s)/(1.6022 10-19C)(0.6600T) = 0.772 m Since the two isotopes have the same speed and are traveling in the same direction, the spatial separation between them after they have traveled through a half-circle will be the difference in their radii, 0.711 m - 0.772 m = -0.061 m.