Cyclotron & Spectrometer

What is a Cyclotron?

A device used to accelerate positively charged particles like protons, alpha ( α ) particles, deutrons, ions etc. to acquire enough energy to carry out nuclear disintegrations, is called Cyclotron.

A Cyclotron works on the principle that –

“When a positively charged particle is made to move through a region in which a high frequency electric field and a strong magnetic field both are present simultaneously, then the particle gets accelerated and acquires sufficiently large amount of energy which then directed to hit a target to perform a desirable task.

Use of a Cyclotron

Cyclotron is used to produce radioactive material for medical purposes e.g. for the purpose of diagnostics and treatment of chronic diseases.
It is also used to synthesize fresh substances.
Cyclotron is used to improve the quality of solids by adding ions.
It is used to bombard the atomic nuclei with highly accelerated particles to study the nuclear reactions.

Construction of Cyclotron

Construction of a Cyclotron is shown in figure. It has following features –

It consists of two hollow $D$ shaped metallic chambers $D_1 \ \text {and} \ D_2$ called “dees”.
These dees are separated by a small gap where a source of positively charged particle is projected.
Dees are connected to high frequency oscillator, which provides high frequency electric field across the gap between two dees.
When dee $D_1$ is negatively charged, dee $D_2$ is positively charged for half of cycle. For next half cycle, the polarity of dees get reversed.
When the charged particles or protons are inside the dees, they are shielded from electric field but magnetic field acts on them. Hence, magnetic field makes them to move in circular paths inside dees.
Magnetic field inside dees are perpendicular to the plane of dees.

Working principle of Cyclotron

Let, initially the dee $D_2$ is negatively charged and dee $D_1$ is positively charged. At this instant, if a positively charged proton is emitted from a source and enters the gap between dees, it will accelerate towards $D_2$ being negative. As soon as it enters the dee $D_2$ , it is shielded from the electric field by the metallic chamber. Inside $D_2$ it moves at right angle to magnetic field and hence describes a semi-circle inside it. After completing the semi-circle, it reaches the gap between the dees.

In mean time, the polarity of dees get reversed and now the proton is attracted and fully accelerated towards $D_1$ . Inside $D_1$ it again describes the semi-circle due to the magnetic field which is perpendicular to the motion of the proton. In this way, the proton goes on moving in circular paths inside dees.

In each cycle of motion in circular paths, the protons accelerated more and its energy increases. This makes the protons to move in larger radius of circular paths. This process continues till the proton reaches the periphery of the dee system. At this stage, the proton is deflected by the deflecting plate attached to the periphery of one dee. Then the proton comes out from dee system through the window and hits the target.

Properties of motion in a Cyclotron

Inside the dee system, proton move in a direction at right angle to the direction of magnetic field $( \vec {B} )$ . Then, inside the dee the magnetic force acting on it is –

$F = qvB \sin 90 \degree = qvB$

This force provides the necessary centripetal force to move the proton in a circular path. Let, the radius of the circular path is $( r )$ .

Therefore, $\quad qvB = \left ( \frac {{mv}^2}{r} \right )$

Or, $\quad r = \left ( \frac {mv}{qB} \right )$

Time taken by proton to complete the semi-circle inside one dee will be –

$t = \left ( \frac {\text {Distance}}{\text {Speed}} \right )$

$= \left ( \frac {\pi r}{v} \right ) =\left ( \frac {\pi}{v} \right ) r$

$= \left ( \frac {\pi}{v} \right ) \times \left ( \frac {mv}{qB} \right )$

$= \left ( \frac {\pi m}{q B} \right )$

$= \left ( \frac {\pi}{q_s B} \right )$

This shows that, time taken by the proton to complete any semi-circle is –

Independent of the radius of circular path.
Depends on the specific charge $\left [ q_s = \left ( \frac {q}{m} \right ) \right ]$ and electric field $( B )$

Therefore, as the radius of motion of circular path increases, the velocity of the proton also increases. That means the proton is always accelerated in the dee system.

Mass Spectrometer

Mass spectrometry or mass spectroscopy are analytical techniques used for identification and segregation of chemical substances. The instruments used in such studies are called mass spectrometers and mass spectrographs.

Working principle of Spectrometer

Mass spectrometers and spectrographs work on the principle that –

“Moving gaseous ions may deflected in the presence of electric and magnetic fields according to their mass per unit charge ratios called ( m/z ) ratio”.

If a gas sample has mass $( m )$ and total charge of $( z )$ , then –

$\text {( m / z Ratio )} = \left ( \frac {\text {Mass of gas sample}}{\text {Total charge of gas sample}} \right )$

Or, $\text {( m / z Ratio )} = \left ( \frac {m}{z} \right )$

( m / z ) ratio of a gas sample is similar to the reciprocal of specific charge $( q_s )$ for charged particles.

Constriction of Spectrometer

A mass spectrometer is shown in figure. It consists of three components –

Ionization Chamber.
Mass Analyzer
Ion Detection System.

1. The Ionization chamber –

Testing sample is converted into gaseous phase ions and directed to move through an external environment of electric and magnetic field.

2. The Mass Analyzer –

Ions are passed to move through analyzer having electric and magnetic field. Ions get deflection based on their mass to charge $\left ( \frac {m}{z} \right )$ ratio. Thus ions are sorted and separated according to their $\left ( \frac {m}{z} \right )$ ratios.

3. Ion Detection System –

These separated ions are then measured and sent to a data processing system where the $\left ( \frac {m}{z} \right )$ ratios are stored together along with their relative abundance and processed to get a spectrum called mass spectrum.

A mass spectrum is simply a plot of $\left ( \frac {m}{z} \right )$ ratios of the ions present in a sample plotted along $X$ axis against their intensities in $Y$ axis.

Use of mass Spectrometer

Mass spectrometers and spectrographs are used –

To calculate the exact molecular weight of a chemical compound.
To identify the unknown compounds, impurities present in chemicals.
Mass spectroscopes are also employed to separate isotopes and to measure their abundance.
This is employed to separate isotopes and to measure the abundance of concentrated isotopes when used as tracers in chemistry, biology, and medicine.
To determine the structural and chemical properties of molecules and ions or charged particles.

See numerical problems based on this article.