Radioactive decay
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RADIOACTIVE DECAY. Berçin Kutluk. Alpha Decay. Why do elements undergo radioactive decay?. Some nuclei are stable, while others undergo radioactive decay. How do we distinguish one from the other?.

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RADIOACTIVE DECAY

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Radioactive decay

RADIOACTIVE DECAY

Berçin Kutluk

Alpha Decay


Radioactive decay

Why do elements undergo radioactive decay?

Some nuclei are stable, while others undergo radioactive decay. How do we distinguish one from the other?

The answer lies in conservation of energy. A nucleus will decay if there is a set of particles with lower total mass (a lower mass will mean less energy and a nucleus having less energy is more stable) that can be reached by decay process or simply by fission, a process in which a massive  nucleus splits into two less massive ones. 

The mass of a nucleus is determined by the sum of the energies of all its constituents. The energies of the constituents depend on their masses, their motion, and their interactions (a process in which a particle decays or it responds to a force due to the presence of another particle, as in a collision).


Radioactive decay

Alpha Decay

and energy conservation

In alpha-decay an atom ejects an alpha particle, which is simply a helium atom without any electrons. In doing so the parent atom decays into a lighter particle. An example of this is a uranium-238 atom decaying into into a thorium-234 atom and an alpha particle (helium-4 nucleus, i.e. 2 protons and 2 neutrons). A schematic diagram illustrates this:

This type of decay occurs naturally in uranium and is an example of "spontaneous decay".

The uranium atom doesn't just break apart. As it decays, each of the two resulting elements (the thorium and α-particle) fly apart at high speed. In other words they both have kinetic energy.

It is possible to measure the mass of the original uranium atom and the masses of the two resultant particles. This is done by measuring the momentum of each particle as it strikes a sensor. When these measurements are taken it is found that the total mass of the two smaller particles is less than the mass of the original uranium particle. Some mass must have been turned into (mostly kinetic) energy.


Radioactive decay

Energy Changes in Alpha Decay

In alpha decay, the atomic number changes, so the original (or parent) atoms and the decay-product (or daughter) atoms are different elements and therefore have different chemical properties.

In the alpha decay of a nucleus, the change in binding energy - amount of energy that must be supplied to break an atomic nucleusinto its component fundamental particles appears as the kinetic energy of the alpha particle and the daughter nucleus.

Because this energy must be shared between these two particles, and because the alpha particle and daughter nucleus must have equal and opposite momenta because of the law of conservation of momentum, the emitted alpha particle and recoiling nucleus will each have a well-defined energy after the decay. Because of its smaller mass, most of the kinetic energy goes to the alpha particle.

To express it more concretely, we know that momentum is the product of mass and velocity of an object. Since alpha particle has a smaller mass, it will take the larger energy – and therefore have higher speed while the decayed element is heavier and will move slower. The momentum at the beginning is zero – assuming that the vibrational energy of atoms is minimum and because of this balance, it will be the same again.


Radioactive decay

ZONE of NUCLEAR STABILITY

As you move higher in atomic number on the periodic table you find that the number of neutrons increases much faster than the number of protons in stable elements. If these elements have too many neutrons they are said to be "heavy". Neutrons do stabilize the nucleus (and thus the atom) blocking the interaction between protons (protons repel each other at a certain distance because of Coulomb repulsion force). Too many (or too few) protons though, makes the atom unstable and that is when, in some cases, an alpha particle is emitted. By emitting an alpha particle the atom is able to increase the stability by reducing the ratio of protons to neutrons. This can be shown simply by saying that a nucleus has 60 protons and 80 neutrons (purely hypothetical). The ratio initially is 0.75 (60/80) but when an alpha particle is emitted the ratio becomes 0.74 (58/78).

The aim of the elements is to enter the stability zone, as in the decay of polonium, in the next example.


Radioactive decay

Too much/few protons make the atom unstable and the atom emits an alpha particle to become stable by reducing the proton/neutron ratio.

210Po84

84/210 = 0.667

The polonium nucleus has 84 protons and 126 neutrons. The ratio of protons to neutrons is Z/N = 84/126, or 0.667. A 206Pb nucleus has 82 protons and 124 neutrons, which gives a ratio of 82/124, or 0.661. This small change in the Z/N ratio is enough to put the nucleus into a morestable state, and as shown in Figure, brings the "daughter" nucleus (decay product) into the region of stable nuclei in the Chart of the Nuclides.

206Pb82

82/124, or 0.661


Radioactive decay

EXPRESSING IT AS AN EQUATION

Alpha decay can be expressed as an equation in which an element X decays to Y, emitting an alpha particle and a discrete energy, in millielectronvolts:

AXZ A-4YZ-2 + α

210Po84 206Pb82 + 4He2 + 3,5MeVα

A small note: As we can see from the decay of polonium, an element becomes stable when it decays into lead. Pb is in fact the heaviest element that is stable. However, elements lighter than Pb can also decay due to an unbalance in proton/neutron ratios.


Radioactive decay

&

the Strong Force

Alpha Decay

What are strong forces?

The nucleus of helium contains two protons. They are both positively charged and will repel each other. So why don’t protons go flying out the atom and stay bound in a helium nucleus? There must be another force that holds them together.

This force is the Strong Nuclear Force.


Radioactive decay

What kind of a force is it?

The strong nuclear force binds protons and neutrons together to make the nucleus.

The strong nuclear force is actually a force between quarks and is carried by particles called gluons – which are force carriers. Protons and neutrons are made of quarks and they feel the strong nuclear force as well.

Protons would fly out of the nucleus due to repulsion if there was no strong force

Think of a force carrier like this. I have a stick in my hand and push my friend with that stick. He/she will fall down – because the force I exerted does work. This force is transferred – or “carried” – by the stick. The stick is a force carrier.


Radioactive decay

“CARRY”ing strong nuclear force

They are called gluons because they “glue” the quarks together.

Gluons are massless, travel at the speed of light, and possess a property called color. Analogous to electric charge in charged particles, color is of three varieties, designated as red, blue, and yellow, and analogous to positive and negative charges - three anticolor varieties. Quarks change their color as they emit and absorb gluons, and the exchange of gluons maintains proper quark color balance.    

Unlike other forces, the force between quarks increases as the distance between the quarks increases. Up to distances about the diameter of a proton, quarks behave as if they were free of one another, a condition called asymptotic freedom. As the quarks move farther apart, the gluons that move between them utilize the energy that they draw from the quark's motion to create more gluons...the larger the number of gluons exchanged among quarks, the stronger the binding force. The gluons thus appear to lock the quarks inside the elementary particles, a condition called confinement. Gluons can also bind with one another to form composite particles called glueballs.


Radioactive decay

But if the strong force is so “strong”, how does an alpha particle get free of the nucleus. The force carriers – the gluons – get even stronger at long distances. Therefore, it seems impossible for an alpha particle to detach itself from the strongly packed nucleus....


Radioactive decay

The RANGE of strong forces...

SF has a very short range (about 10-15 metres - the size of the nucleus. And the attraction of quarks is at proton and neutron level (it is predictable that when neutrons are too much the balance is disturbed)

- Because of this, only very close to the nucleus can the proton feel its attraction. The range of the electric forces (which are pushing out) are much bigger.

- If a sudden position change in nucleus occurs, the balance between these forces

İs upset and the elctric force dominates; activating the proton-proton repulsions and causing a part of the nucleus to break

free.

- In fission, for example, the nucleus can break more or less in half.


Radioactive decay

But WHY helium?

The "binding energy" of a particular isotope is the amount of energy released at its creation; you can calculate it by finding the amount of mass that "disappears" and using Einstein's famous equation. The binding energy is also the amount of energy you'd need to add to a nucleus to break it up into protons and neutrons again; the larger the binding energy, the more difficult that would be.

It happens that the 4He nucleus is held together exceptionally tightly--it has a much larger binding energy than other light nuclei. This makes alpha particles the easiest type of clump to spit out.


Radioactive decay

Breaking out of the nucleus...

Particles can appear in places where energy can't move them, for example,water in a cup does not have the energy to push itself up over the lip of the cup. However, in the microscopic world, particles can appear in places where energy can't take them. For instance, the alpha particle of the element radium can move itself away from the atomic nucleus and through the outside of the nucleus – we know that this is alpha decay itself.

For particles, the surface can appear to be like a wall. Particles in an atomic nucleus do not have enough energy to break through surface tension. However, particles do have wave energy and they use this energy to break through surfaces and exit the core. As the process appears like the particle has traveled through a tunnel in a mountain, it is given the name "tunnel effect."


Radioactive decay

...the tunnel effect.

Alpha-Decay Theory confirmed the mysteries of quantum mechanics. When two objects approach each other their atoms touch at the point closest to the other object. At that moment, the nature of the electrons surrounding the objects' atoms are slightlychanged, each taking on some characteristics of the other – such as energy.By electromagnetic repulsions, the alpha particle can break free of the nucleus and its strong force. This is known as the tunnel effect and was first proposed by George Gamow, the originator of the Big Bang theory, in 1928.


Radioactive decay

How deep can they go?

Once the alpha particle is free from the tight grip of the nucleus you may wonder how long does it last on its own? How deep can it penetrate into say human skin?

These are important questions when dealing with radiation. Alpha particles usually have energies ranging from 4MeV to 10MeV. This amount of energy is not sufficient enough to even pass through paper. To compare to some of the other types of radiation, beta decay can emit a particle (electron) that has an energy of 200MeV which could pass through 17cm of aluminum and gamma decay emits a a photon of energy that could probably pass a meter or more into the aluminum. Thus it can be said that alpha particles are of relatively weak energies compared to other types of radiation...


Radioactive decay

SPONTANEITY OF ALPHA-DECAY

-Alpha decay is an exothermic process. As the nucleus becomes more stable, it liberates a net amount of energy due to this. Therefore, the tendency for minimum enthalpy is fulfilled.

-Also, the decay’s entropy can be said to be positive; the places the particles can exist increase (i.e. the micro states increase). A clump from the nucleus is released, making the number of particles two. Particles accelerate suddenly to conserve their momentum – randomness per unit time increases. Therefore, alpha decay also satisfies the tendency or maximum randomness.

Under these conditions, it can be said that Alpha decay is always spontaneous.


Radioactive decay

SMOKE DETECTORS

...an interesting use of alpha radiation

One interesting use of alpha decay can be found in smoke detectors, which seems like an unlikely place. Smoke detectors contain the radioactive isotope americium-241 which was obtained from the decay of plutonium. Alpha particles from the americium collide with oxygen and nitrogen particles in the air creating charged ions. An electrical current is applied across the chamber in order to collect these ions. When there is smoke in this chamber the alpha particles are absorbed by the smoke. This lowered the number of ions in the air and thus the electrical current is reduced setting of the alarm. Americium-241 is quite safe because the alpha particles usually travel only a few centimeters in air.       


Radioactive decay

THE SMOKE-DETECTOR

Figure shows a simplified set up of a smoke detector (not including the alarm mechanism and I'm sure some other important pieces).   


Radioactive decay

Rutherford – the first successful

alchemist

• Transformed N to O

– 14N + a17O + 1H

• Why wouldn’t it be practical to convert Pb

into Au?

• The conversion of platinum into gold has

been achieved by bombarding platinum-198

with neutrons to produce platinum-199.

This isotope, in turn, decays to gold-199

with the loss of a subatomic particle. What

subatomic particle is lost by the platinum as

it becomes an atom of gold?


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