  # Determination of relative atomic masses of isotopes by Dempster’s mass spectrometer

Different steps involved in the determination of exact atomic masses and the relative abundances of different isotopes of an element are given below:

## 1. Vapourization:

The substance, whose analysis for the separation of isotopes is required, is converted into its vapours. The pressure of these vapours is kept low in the range of 10-6 to 10-7 torr.

## 2. Ionization:

These vapours are then allowed to enter the ionization chamber where they are bombarded with high speed electrons. As a result of this bombardment, the atoms or molecules present in the vapours will be ionized. The resultant positive ions will have different masses.

Their masses will depend upon the nature of the isotopes present in the given sample of the element. Different isotopes of the same element will have different masses and different m/e values.

## 3. Acceleration-of positive ions:

These positive ions are accelerated by passing them through an electric field. For this purpose, a potential difference (E) of 500 to 2000 volts is applied between the accelerating plates. These positive ions are strongly attracted towards the negative plate. In this way, these ions are accelerated.

## 4. Separation of Ions:

The beam of accelerated positive ions is then allowed to pass through a strong magnetic field of the strength H. This magnetic field is applied in a direction which is perpendicular to the path of the positive ions. The applied magnetic field will help us in these separation of positive ions on the basis of their m/e values.

The magnetic field makes the ions to move in a circular path. The ions of definite m/e value move together in the form of groups. In this way, one beam containing many types of isotopes splits up into more than one type of beams. Each beam contains only one type of isotope.

## 5. Mathematical explanation:

The mathematical relationship between m/e values and deflection in the circular path is:

[latex s=3]\frac{m}{e}=\frac{H2r}{E}[/latex]

Where,

H = Strength of the magnetic field.

E = Strength of the electric field.

R = Radius of the circular path.

## 6. Relative Abundance of Isotopes:

The accelerating potential is so adjusted that the positive ions or isotopes of a particular mass to charge ratio are focused through a slit to the surface of an electrometer. Hence each positive ion gains an electron to neutralize itself. This will produce an electric current in the electrometer circuit. The strength of this current is measured. The strength of this current gives the relative abundance of the particular isotope.

The acceleration potential is then readjusted so that the particles of another isotope are made to pass through the slit and then to the surface of the electrometer. Again electric current is produced and its strength is measured. This current strength will give the relative abundance of the second isotope and so on.

The current strength in each case gives us the relative abundance of each isotope in the given sample. If the number of ions of a particular isotope is greater than more current will be produced and we shall get a higher peak for that isotope in the graph.

## 7. Comparison with Carbon – 12:

The same experiment is repeated with Carbon – 12 and the current strength is compared with those of the isotopes. This comparison will help us to know the exact relative atomic masses of the isotopes in the given sample.

## 8. Modern Spectrograph:

In modem spectrograph, each ion strikes a detector the ionic current is amplified and is fed to the recorder. The recorder makes a graph show in the relative abundance of isotopes plotted against the mass number.

## 9. Separation of isotopes:

Since isotopes of an element have same chemical properties, so they cannot be separated by chemical methods. Following physical methods are used for their separation:

1. Gaseous diffusion
2. Thermal diffusion
3. Distillation
4. Ultracentrifuge
5. Electromagnetic separation
6. Laser separation

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