This article will see how mass spectrometry works and how the force equation F=qVXB can answer the question.

## What is Mass Spectrometry?

### Mass spectrometry Definition

It a technique used to measure the mass-to-charge m/q or q/m ratio of ions analytically. We present the result as a mass spectrum- a plot of intensity vs the q/m ratio.

Image courtesy: BronkHorst

## 1. Introduction to mass spectroscopy and the use of F=qVXB

The force (magnetic) on a charged particle is F=qVBsin(θ) in scalar notation, and in vector notation, it is F=qVXB where X is the cross product and F, V, B are vector quantities.

The symbols have their usual meanings.

F=magnetic force

V= Velocity

B= External magnetic field

q=charge

θ=angle that velocity vector makes with the external magnetic field B.

## 2. Identify the charge q that is moving

We bombard the sample with fast-moving electrons and generate charge q. The moving electrons hit the sample atoms and knock out electrons from their outer shells, making the sample atoms charged. This charge is necessary because we can not impart high speed using the high potential difference unless the atoms are charged.

## 3. Identify the velocity that describes the motion of the charge

We apply a very strong EMF to the sample, converting it to ions. It imparts a force on the ions given by F=qE, where E is the electric field associated with the applied potential. Let it move by a distance d in this electric field E. So work done is qEd. This work must equal the change in kinetic energy as energy is not lost anywhere. So 1/2mV^2=qEd So V=(2qEd/m)^0.5. It is how the velocity comes into the picture.

## 4. Identify the magnetic field B that the charge feels

We apply an external magnetic field to the setup via high-power electromagnets. This B is normal to the motion of the charges (θ=90 degree, so sin(θ)=1.

## 5. Calculation of net force

We saw that F=qVXB

Here

q= charge on the ion

V= V=(2qEd/m)^0.5 as calculated earlier.

B= External magnetic field, which acts at θ=90 degrees (normal) to the velocity vector.

Using the vector cross product rule, F magnetic is F=qVBsin90=qVB

Direction is normal to the plane containing both V and B vectors and determined by the right-hand rule.

F=qB(2qEd/m)^0.5

## 6. Explanation of this force F in context of the problem

Force F is equal to m*V^2/r where r= radius of the circle in which the ions bend when they pass through the external magnetic field. So,

qBV=m*V^2/r

Using this, we can get

r=mv/qB where V=(2qEd/m)^0.5

We can see clearly that except for mass “m,” all the things are the same for each ion. The ion with more mass will have a larger radius, “r,” and will bend lesser.

Using this, we can determine the kind of mass distribution the sample has. We see the density on the detector to make out the fraction of ions which got bend more or less. A typical mass spectrometry spectra is shown below for reference.

So this was the theory behind mass spectrometry. If something is not clear, feel free to comment in the comment section below. We will be pretty happy to answer all your questions.