Picture 2.02
As more protons and neutrons unite in an atom of heavier elements, then their closiness reduces as they begin tightly to pack in the nucleus. As the tight connection between protons in the nucleus enlarges or the distance between protons decreases , it takes about sixteen nucleons (protons and neutrons)to be in the nucleus of an atom to reach the size of 2 and a half of the proton’s diameter. When the diameter of the atomic nucleus reaches that size, then strong nuclear forces start to lose their strength and an electromagnetic force takes dominance. The last element in the periodic table (from the smallest to the higher atomic number) which is still stable is iron as strong nuclear forces and electromagnetic forces are in a kind of eqilibrium or have an equal effect so the nucleus of iron is still stable. However, it is not before an atom reaches a mass of around 207 that it becomes so unstable that it starts spontaneously to decay. When this process starts, it takes the form of emitting particles (alpha, beta particle), energy (gamma rays) or splitting into 2 so-called daughters or 2 atoms with stable atom mass which is smaller than it was in the mother atom or initial atom, the process called fission.
Alpha radioactive decay is the spontaneous decay of an atom where alpha rays or particles are emitted. Alpha particles are the nucleus of a helium atom, having an atomic mass of 4 and atomic number 2 (they consist of 2 neutrons and 2 protons). During such a process, the initial element loses its mass by 4 and an atomic number by 2. The final result will be a new element with reduced atomic number by 2 and mass by 4.
Uranium with the atomic number of 92 and mass of 238 decays, emitting alpha particle or helium nucleus of atomic number 2 and mass 4 and gives another element thorium with atomic number 90 and atomic mass 234.
238
4
234
U
=
He +
Th
92
2
90
In this equation of alpha decay of uranium to thorium we can demonstrate again the conservation of the baryon number. The mass and atomic number of uranium is equal to the sum of the atomic number and masses of helium and thorium.
Unlike beta decay, alpha radioactive decay is not the result of weak nuclear interaction where W or Z virtual particles play a role. Instead, it is caused by so- called quantum tunnelling.
Quantum tunnelling refers to a particular property of subatomic particles where the particles can go through a barrier with no additional energy needed for this to happen.
We can use the analogy of playing with a tennis ball which we are repeatedly throwing against the closed door. In each case, the tennis ball will bounce back from the closed door. It will not go through the door. In order to do so, the ball needs to have much more energy. If we put the ball in a gun from where the tennis ball can be fired at the speed of a bullet, then the ball can pass through the closed door making a hole in it. In other words, it does have enough energy to pass through this barrier.
In a world of subatomic particles where distances and particles are fantastically small, different rules are applied. The movement and the position of subatomic particles do not follow the rule of classic mechanics, which is applicable at great distances in the world we know. They follow the rule of quantum mechanics.
What does that mean?
Well, we can say that unlike in our world where we can easily define the position and the momentum of an object, such as a tennis ball (meaning the ball’s location and its movement), this is not possible in a micro world where subatomic particles rules the world. Electrons, protons or atoms can be in any position and have any movement. There is, therefore, a great uncertainty as to where any particular particle is located, or rather to say, it could be located anywhere. This, however, implies the possibility that a particle can also be found on the other side of the barrier, which means that the particle has to pass the barrier with no use of any extra energy. This is actually quantum tunnelling.
With such unlimited possibilities of the particle’s location or rather the uncertainty of its location, quantum mechanics helps to calculate the probability that a particular particle will be at a certain place, including the probability that it will be on the other side of the barrier; in other words, the probability that quantum tunnelling will take place.
It was Richard Feynman, an American theoretical physicist, who developed the part integral formulation and an equation, which is helpful to determine the probability that a particular subatomic particle will be at a certain position.
Professor Brian Cox, a physicist, has outlined a simple version of Richard Feynman’s equation in a TV documentary A Night with the Stars. That was regarded as a full lecture delivered to a celebrity audience in Manchester and was aired on the BBC. The programme can be easily found on YouTube and I would strongly recommend it.
In this programme Prof. Brian Cox outlined a simple version of Feynman’s path to integral formulation. He wrote a formula of a time needed for quantum tunnelling to take place or the probability that after a certain time the particle or object can be on the other side of the barrier. According to an outlined equation, the time needed for this to happen depends on the product of the distance we expect the object to jump, the size of the place where this object is located and the mass of this object divided by the Planck constant.
x is distance to jump, dx is the size of the location where the object is positioned and m is the mass of an object while h is the Planck constant which is 6.6 x 10 on power of –34.
As all matter is composed of atoms and atoms follow the rule of quantum mechanics, then every object, does not matter how large or massive it is, can have a probability to be located on the other side of a barrier at one point in time. The time needed for this possibility to happen depends on the size of a location in which an object is placed, the distance it needs to jump to be on the other side of the barrier and its own mass.
In the case of a tennis ball to be found on the other side of the closed door, we calculate the size of the room, say it is 4 metres, and multiply this with the distance we want the ball to be in order to be outside the closed door. That could be 4 metres and 20 cm, for instance. We then multiply all of this with the mass of a ball, say 10 g, and then we divide this with a Planck constant. The result obtained is the time needed for the ball once to be found outside the closed door during our time of throwing the ball on the wall. I have no intention of making this calculation here. Instead, I will use an example Prof. Brian Cox gave in the documentary programme mentioned. He used the example of a diamond being in a box of 5 cm, wanting to calculate the time needed for the diamond to be found 6 cm away (meaning outside the box) with the mass of diamond being 60 grams. The product of these values divided by the Planck constant has given the result of 3 x 10 on power of 29 seconds which meant that this number of seconds was needed for the diamond to be found 6 cm away or outside the box. Prof. Brian Cox outlined that this number of seconds was equal to a 600 billion times the current age of the universe. Such a long time is due to such a small number of the Planck constant. If, however, the size of location of the object, together with mass of the object and size of the distance needed for the object to jump is incredibly small as in the case of subatomic particles, then the time for the particle to be on the other side or for quantum tunnelling to take place is not so long. It happens therefore more frequently.
Quantum tunnelling is therefore what facilitates alpha radioactive decay.
Quantum tunnelling also facilitates the nuclear fusion process as much as weak fundamental interaction.
The fusion of hydrogen nucleus into helium nucleus takes place in the centre of a star. In a star’s core there is very high pressure and temperature,
which gives high energy input to hydrogen atoms and electrons rotating around its nucleus, which consists of one proton. This high energy, thanks to the high pressure and temperature, makes an electron jump from a lower energy level to the higher energy level of a hydrogen atom (it jumps from a shell closer to the atom to a shell further from the atom). As the temperature is very high and therefore energy, an electron moves in cascade from the first to the last shell, the 8th shell. Eventually, with constantly high energy, en electron jumps from the last shell decupling itself from the hydrogen atom. The hydrogen atom has lost its structure and we have now plasma formation consisting of protons and electrons. Also, protons now move rapidly in all directions; they are prevented from coming close to each other due to electromagnetic force and consequent repulsion among each other. The barrier of this repulsion is the distance among two protons equivalent to the sum of radius of 2 and a half protons. It is thanks to quantum tunnelling that protons find themselves on the other side of the barrier or at a distance less than 2 and a half of radius of proton (Pic 2.02). Once they are within this distance they are captured by strong nuclear fundamental interaction, which are strong within this radius. That is how and why Quantum tunnelling is important for nuclear fusion to take place.
Beta radioactive decay takes place when weak fundamental interactions are involved. Depending whether W and Z bosons change down to up quarks or up to down quarks, we have Beta-minus decay of Beta-plus decay respectively.
Beta-minus radioactive decay is a process where the neutron of an atom is transformed into a proton and emits negatively charged electrons and antineutrino. Bosons of weak fundamental force or mesons change the flavor of down quarks to up quarks, transforming neutrons (2 down+1up quark) into protons (1 down+2 up quark). Electron and antineutrino is emitted. Here, the initial atom has the same mass as the daughter atom which is the end product of this decay but increased atomic number by 1. An example is beta-minus decay thorium with mass of 234 and atomic number 90 to protactinium with mass of 234 and number of 91.
ē is electron while v̅ is antineutrino
Beta-plus radioactive decay or positron emission does not occur among naturally present isotopes but does take place among artificial ones made by humans. Here, mesons of weak fundamental interaction, virtual particles or bosons change up quark to down 1, transforming protons into neutrons. The final product is an element with the same mass but reduced atomic number by 1. It emits positron (positively charged electron) and neutrino. The beta particle in this case is positron. It is a case of artificially made isotope of kalium (potassium) and its decay by beta-plus radiation to argon with the same mass and reduced atomic number from 19 to 18 (by 1).
Electronic capture is a similar process to Beta-plus radioactive decay. The difference is that there is no positron emission and that an electron from the cloud or orbital next to the atomic nucleus is captured and fused with a proton in the nucleus, giving a neutron. As the orbital from where an electron is captured is now empty, the atom is in an excited state. An electron from the other orbital takes the place of this electron, which is captured, bringing down an atom in a ground state. In this process, x-ray is emitted.
Gamma decay is radiation, which can be emitted following alpha, or beta decay or it can happen on its own. It is the result of newly produced atoms being in an excited state and its tendency to go back to ground state. During this process, energy is emitted in the shape of gamma rays. Atomic nuclei can be in an excited state on their own. In such a case, when they return to ground state they emit gamma rays. High energy level within the nucleus itself is not understood well as high energy levels of electrons. As we know, high energy levels of electrons are referred to as quantum energy levels which are described as shells around an atomic nucleus. In a similar way, an atomic nucleus has a different quantum energy level where protons can go on a higher energy level of being excited. In such a state, protons tend to go back to a low energy level or ground state, as this is a natural law in the universe. In this process of going back to ground state, they emit gamma rays.
Spontaneous fission is a type of radioactivity where the nucleus of a heavy element splits into two roughly equal newly created nuclei, each of which is around half of the mass of an initial heavy atom. This process happens very rarely among natural heavy elements such as uranium but does happen among artificially created heavy elements such as fermium-256. In the process there are always a few neutrons that are left out. Due to the acceleration they got in the process of splitting of an initial atom, they hit other atoms, causing them to become unstable and split. This acceleration is due to the strong repulsion of split atomic nuclei due to their same charges and the fact that 2 newly formed nuclei are now at a distance more than 2 and a half radius of proton where strong repulsive forces of electromagnetic force dominate. As neutrons accelerate as well they can hit and reach the inside of new nucleons causing them to split by emitting new free neutrons which will hit other atoms causing them to split. That is a chain reaction.
Otto Hahn, German chemist, and Fritz Strassmann, German physical chemist, discovered nuclear fission in 1938 around Christmas time. Following this discovery and further progress in nuclear physics, an atomic bomb was created. On 16th July 1945, the first atomic bomb was tested near Alamogordo in southern New Mexico.
On 6th August 1945 the atomic bomb was used as a weapon for the first time. It was dropped on Hiroshima, instantly killing around 70 000 people with the number rising above 100 000 by the end of the year. The second bomb was dropped two days later on 9th August 1945 on Nagasaki. It killed around 40 000 people. It marked the end of the Second World War.
ELECTROMAGNETIC FUNDAMENTAL INTERACTION
After strong nuclear force, electromagnetic nuclear force is the most powerful force among the three remaining ones, including electromagnetic force itself.
Unlike other forces, it refers to the interaction between charged particles, protons and electrons, and does not affect neutral particles, neutrons. This fundamental interaction takes place with the help of virtual particles (bosons or photons or light particles) which exchange communication between particles telling them to attract to each other or repulse depending whether they are the same or opposite charge. When two electrons are on the path of collision, a virtual practical photon is created. Photons inform particles (electrons) that they should repulse each other as in the diagram known as: Richard Feynman’s diagram.
Picture 2.03
An electromagnetic force keeps the structure of the atom together as well as that of complex structures such as molecules. By doing this, it helps matter to appear in different shapes and forms including leaving world and us.
The strength of the forces is, as with gravitational forces, inversely proportional to the squared distance between particles affected by the force.
Looking from the aspect of classical physics, electromagnetic force is the combined force of two phenomena, which occur in the universe: electricity and magnetism. Perhaps the best way to describe electromagnetic force in relation to electricity and magnetism is if we refer to the electromagnetism as a coin with two sides: one electricity and one magnetisms.
Both electricity and magnetisms were known well before it was realised that these two phenomena are interconnected. It was not until the 19th century that these two phenomena were seen as united forces of electromagnetisms. There were three crucial historic events, which help us understand the connection:
1.Accidental discovery confirming the relationship between electricity and magnetism. Hans Christian Orsted, a Danish physicist and chemist, noticed that a compass needle deflected from magnetic north when it was closed to electric current. This discovery was made during winter in 1819-20. He is regarded as the first scientist to notice this connection. However, it was an Italian scientist and philosopher, Gian Domenico Romagnosi, who first noticed a magnetic effect of a current in 1802. His work was published in a newspaper, which was
not so popular, and his work was overlooked by scientific society at that time.
2.Michael Faraday discovered that he could produce electricity from changing the magnetic field. He performed this experiment of inducing current by changing the magnetic field in 1831.
3.James Clark Maxwell gave the final touch to comprehension and realisation of the existence of combined electromagnetic force. Through experiments and his equations, Maxwell realised that a change of electric field produces a change of magnetic field, which in turn causes a change in electric field and vice versa. He predicted the existence of electromagnetic waves, which propagate through space at the speed of light. It was finely understood the nature of light. The light was nothing more or less than electromagnetic waves with a frequency of waves or their wavelength within the spectrum of visible light.
As electricity and magnetism were known well before electromagnetism was discovered, I would like to pay brief attention to each of them with a brief history of the events which shape our knowledge and understanding of these phenomena through the centuries.
Journey Through Time Page 5
