Understanding how mass spectroscopy works

Question

Let me start by saying that I've posted this question here as well. I've posted it here because I think the questions I've asked involve the physics of molecules.

So I’m trying to get a deeper understanding of how mass spectroscopy works. Most tutorials and textbooks I’ve encountered omit certain details about the process and I’m hoping someone out there who understands the process can fill in the gaps. I’ll start by explaining the way I currently understand the process and then list where I start to get confused.

1 First a particular molecule is bombarded with a beam of electrons (ionization step). This step works to free an electron from the molecule under analysis which generates a cation.

Note: It’s important to remember that the only reason why this molecule was ionized is to make use of a magnetic field to bend its direction. Only ions will be affected by this magnetic field which allows us to pinpoint the molecule in question.

2 Next, these ions are accelerated by an electric field toward a magnetic field that bends the moving ions by a certain amount.

Question 1: What’s the difference between an electric field and a magnetic field? And why does the magnetic field bend the ions while the electron field does not. Is this just a consequence of the shape of the apparatus? Could you use a magnetic field to accelerate a particle and a electric field to do the bending? I’m just really confused as to the difference between electric fields and magnetic fields.

3 The ions that bend will travel around a tube by a certain degree and hit a detector. The amount of bending will tell us about the mass of a particular molecule. Heavier molecules will bend less and lighter molecules will bend more.

Question 2: I’ve come across a tutorial that said that what this detector is actually measuring is the mass to charge ratio. How is this calibrated and how does this step allow us to measure the mass of a single molecule. Won’t there be multiple particles hitting the detector at the same time, will this not affect the mass reading of a particular molecule? I'm just confused about this final step and how we can get an accurate mass reading for a particular molecule.

Any help understanding this concept would be appreciated.

Answer 1

Regarding your first question, a magnetic field will not normally speed up a particle as it can do no work on it, while an electric field can both accelerate it and bend its path, depending on the configuration. An electric field along a particle's velocity will accelerate it, while an electric field orthogonal to it will bend the path. The maths behind this is the Lorentz force, $$\mathbf{F}=q\left(\mathbf{E}+\mathbf{v}\times\mathbf{B}\right),$$ where the magnetic component is always orthogonal to the velocity. If you are still confused about the roles of electric and magnetic fields I'd recommend you read the introductory sections of Griffiths or the like.

This leads directly to the fact that it is only the charge-to-mass ratio that enters the equation, since from Newton's 2nd law, $\mathbf{F}=m\mathbf{a}$, the equation of motion is $$\mathbf{a}=\frac qm\left(\mathbf{E}+\mathbf{v}\times\mathbf{B}\right),$$ where only $q/m$ enters. Bigger masses mean smaller $q/m$ ratios which mean smaller effective fields and less impact on the trajectory, which then bends less. This is not really a problem in calibration since charges are typically small multiples (i.e. one or two times) of the electron charge, and this causes easily distinguishable peaks that correspond to different charge states.

If there are multiple particles hitting the detector at the same time, then they will hit it in different spots if they have different masses, which will make two different pixels light up (and we can then distinguish them and treat them independently). The only problem occurs when multiple ions of the same charge and mass hit the detector in close succession, in which there is a danger of undercounting (i.e. counting just a single hit). This must be avoided by using integration times smaller than the typical hit-to-hit time.