A beam of singly ionized carbon atoms (C-12, C-13, and C-14 isotopes) is injected into a mass spectrometer, which isotopes would follow the trajectory of greatest diameter and strike the detection plate furthest?

I know the answer is C-14, but why? can someone explain it please :( i have an exam coming up and i dont understand the concept but i know it has to do with velocity selector also. is it because the mass spectrometer separates ions according to their mass to charge ratio, so since C-14 is heavier compared to C-12 and C-13 it would strike the detection plate furthest?

the curvature of the trajectory is related to the mass/charge ratio

the charges are equal ... C-14 has the greatest mass

Yes, you are correct! The concept involved here is the separation of ions according to their mass-to-charge ratio in a mass spectrometer. C-14 will indeed follow the trajectory of greatest diameter and strike the detection plate furthest.

To understand why that is the case, let's break down the process step by step:

1. Ionization: The beam of singly ionized carbon atoms is injected into the mass spectrometer. This means that one electron is removed from each carbon atom, resulting in a positively charged carbon ion.

2. Acceleration: The positive carbon ions are accelerated in an electric field, imparting them with kinetic energy. The amount of kinetic energy given to each carbon ion is dependent on their charge-to-mass ratio, which is the ratio of the charge of the ion to its mass.

3. Deflection: After acceleration, the carbon ions enter a region called the velocity selector. This region contains both electric and magnetic fields. The electric field serves to select ions of a specific velocity, while the magnetic field helps to deflect ions based on their mass-to-charge ratio.

4. Trajectory separation: The ions that have the selected velocity will not be deflected by the magnetic field and will continue in a straight path. However, ions with higher or lower mass-to-charge ratios will experience a deflection due to the magnetic field. The extent of deflection depends on the specific mass-to-charge ratio of the ion.

In this case, since the mass-to-charge ratio of C-14 is greater than that of C-12 and C-13, it experiences a greater deflection. Therefore, C-14 will follow a wider trajectory compared to C-12 and C-13, and it will strike the detection plate furthest from the center.

It's worth noting that the separation capability of a mass spectrometer depends on various factors like the strength of the magnetic field and the design of the instrument. Nonetheless, in general, heavier ions will experience a greater deflection compared to lighter ions, allowing for the separation and identification of different isotopes.