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Journey to the nucleus

# "Since the ancient Greeks..." – the journey to the nucleus

About 2500 years ago, Democritus, the ancient philosopher hypothesised that the world is built from small particles that cannot be divided further. He called them atoms, which means "indivisible" in ancient Greek.

Democritus

Based on observations and experiments, the scientific world accepted the existence of atoms after 1900. It was a slow process because atoms are so small that they are not really tangible and we cannot see them even with microscopes. Only 100 grains of sand contains more atoms than the entire Sahara desert.

We can classify atoms on the basis of their chemical properties. These groups are the elements. Every element has its own chemical properties, but they are not divisible by chemical methods (unlike chemical compounds like molecules). In nature, we can find 94 different elements in smaller or bigger quantities (from hydrogen to plutonium).

Atoms are the building blocks of the universe: every creature, the objects around us, and the distant stars are all made up of them. It is a miracle, that 94 different elements have been able to make such a colourful and interesting world.

In 1897, J. J. Thomson discovered the electron.

J. J. Thomson

This tiny negatively charged particle comes from the inside of the atom.

# The mystery of the atom

Thanks to the brilliant experiments of E. Rutherford between 1909 and 1911, it turned out that the atom has a so called "nucleus", which is in the middle of the atom. It's really dense, and its mass is roughly equal to the mass of the atom.

E. Rutherford

The electrons move around this nucleus, which is about 1/100000 times the size of the atom. If we magnified the atom to a sphere as big as the size of a room, the nucleus would be a grain of dust in the middle...

In the next two decades they found out that the nucleus is consisted of two different particles: positively charged protons, and neutral neutrons. Since 1940, scientists have discovered and created more than 20 new elements (transuranium elements).

The chemical quality of an element is determined by the number of protons in its nucleus. This is the atomic number of the element, denoted by Z. We call protons, and the roughly same heavy neutrons, together as nucleons. The number of nucleons is the mass number (symbol A). The conventional notation of atoms: $$_{atomic number}^{mass number}ChemicalSymbol$$ – in general form: $$_Z^AX$$ – for example, in the case of Uranium: $$_{92}^{238}U$$

The atoms of an element are not necessarily identical: the number of neutrons can differ for a given proton-number. Elements, which have the same number of protons but different number of neutrons, are called isotopes.

E.g. some isotopes of carbon:
 $$_{6}^{11}C:$$ 6 pcs of protons and 11 – 6 = 5 pcs of neutrons $$_{6}^{12}C:$$ 6 pcs of protons and 12 – 6 = 6 pcs of neutrons $$_{6}^{13}C:$$ 6 pcs of protons and 13 – 6 = 7 pcs of neutrons $$_{6}^{14}C:$$ 6 pcs of protons and 14 – 6 = 8 pcs of neutrons

Isotopes are not equally common in nature (with its 98.9 % occurrence $$_6^{12}$$C is the most common isotope), but they can build into a CO2 molecule, our DNA, and all other carbon-compound the same way. – Thus, atoms with isotopic nuclei are chemically indistinguishable and they form compounds the same way with the atoms of other elements. However, there are a few differences in their physical properties. For example, their mass is different. This is analogous to LEGO blocks, with the same size but with different colour, that are interchangeable in a building process:

# Let’s build a nucleus!

There are multiple interactions working between the nucleons. The gravitational force is too weak to be able to compensate for the electrostatic repulsion between the protons. If only these two interactions existed, there would not be atomic nuclei, and the universe would look vastly different.

The repulsion between protons is overcome by the nuclear force (or residual strong force). This force emerges between any two nucleons, which are close enough to each other, and it manifests itself in strong attraction. Fortunately, the range of the residual strong force is really small, so it cannot contract all of the matter in the universe into one giant "nucleus"...

The energy originating from the above mentioned interaction is called the total energy (symbol: E). We can think about this energy as some kind of "glue" that has to be overcome if we want to decompose the nucleus into nucleons.

According to this, nucleons are in a bound state inside the nucleus. In order to separate them, to make them free again, we have to do work (just like when a golf ball falls into a hole, we have to do work in order to take it out of the hole, if we want to play with it again). The nucleons are in a similar potential-hole. Due to their bound state, the total energy of the nucleons is negative.

Now, imagine that we have multiple pieces of LEGO blocks, spread on a table. Let’s measure their masses and calculate the sum of it. After this, we build a toy car, using all of the pieces.

The mass of the car is going to be exactly the same as the summed up mass of the individual pieces, that we measured before. There is only one problem: the nucleus does not work that way! The mass of the nucleus does not equal the mass of the separate nucleons. It is actually smaller.

We call this phenomenon mass defect. In fact, this really strange phenomenon was the first proof of Einstein's mass-energy equivalence. The "lost" mass is equal to the total energy of the nucleus:

$$E=\underbrace{(m_{nucleus}-Z*m_{proton}-(A-Z)*m_{neutron})}_{massdefect}*c^2$$

From the above, we can see that this energy is negative: E < 0

Usually, more complex nuclei (e.g. $$_{92}^{238}U$$) have more binding energy than simple ones (e.g. $$_7^{14}N$$), so we need more work, to take apart them. This isn't so surprising. However, it is interesting, that the nucleons in the different isotopes are not bound in the same form. As if they were not fixed with the same quality glue. It means that the different isotopes are not equally stable. This simple fact has such serious consequences that not only shaped the history of the last 80 years, but it is going to influence our future as well.

# Nuclear landscape: The energy valley

We can characterize the stability of the nucleus with the average binding energy per one nucleon, marked with E/A.

We investigated the average binding energy per nucleon in the 1416 isotopes of the first 94 elements. If we represent this quantity on a 3 dimensional bar graph as a function of the atomic number and the mass number, we get a graph that’s shape looks like a river valley. This is called the "energy valley". We named the physical model created by us "stability object".

At the bottom of this valley, we can find the $$_{26}^{56}Fe$$, the $$_{26}^{58}Fe$$ and the $$_{28}^{62}Ni$$ isotopes. The average binding energy for these nuclei is approximately -1.37 pJ. The lowest position means, that the nucleons are the most strongly bound in these isotopes, so these are the most stable nuclei.

One of the main principles of nature is the principle of minimum energy. (Just think about a ball, which rolls down on a hill-side!) This principle prevails in the world of atoms – with some strict conditions. Nuclei can go through such transformations, that shift their binding energy closer to the value of $$_{26}^{56}Fe$$ . In other words, every nucleus "wants to be iron".

One of the main consequences of the energetically more favourable status is the change in the composition of the nucleus. The nucleus of a new element comes into existence, thus a new atom is created with all of its new chemical qualities. We can illustrate this on the "energy valley" in a simplified way: as the nucleus - just like a ball that rolls down on a hill-side - "jumps onto the top of a lower column from the top of a higher column". In this process, there is no energy loss. The energy lost by the nucleons transforms into the kinetic energy of the emitted particles and/or takes the form of high energy electromagnetic radiation.

This phenomenon was discovered by M. Curie, P. Curie and H.Becquerel, in 1896. Madame Curie named it radioactivity.

 H. Becquerel M. Curie P. Curie

The transformation of the nuclei became important to humanity because, during this process, picojoules ($$10^{-12}$$J) of energy is released, which is a million times as much as in the case of burning. The exothermic chemical reactions (eg. oxidation) give "only" attojoules ($$10^{-18}$$J) of energy to its environment. (This latter reaction takes place in the electron shell.)

# A tour in the energy valley: Nuclear Transformations

In $$\beta^{-}$$-decay one of the neutrons in the nucleus transforms into a proton, while it emits an electron ($$\beta^{-}$$ particle) and an anti-neutrino ($$\bar v$$).

$$_Z^AX \to _{Z+1}^AY+\beta^{-}+\bar{v}$$

This type of transformation can be observed in those isotopes that have neutron-excess compared to the proton-neutron ratio of stable nuclei with the same mass-number. The atomic number increases by 1.

Let's review some examples!
• The $$^{14}$$C isotope, which is used for the dating of organic archaeological findings, decays into nitrogen:
$$_{6}^{14}C \to _{7}^{14}N+\beta^{-}+\bar{v}$$
• Most of the radioactive decays, which happen in the human body, are from the decay of $$^{40}$$K (300-400 decay per second per kilogramme). This radioactive nucleus causes 10-12 % of the unavoidable natural radiation exposure of the civilian population. The product of this decay is calcium:
$$_{19}^{40}K \to _{20}^{40}Ca+\beta^{-}+\bar{v}$$
• In the following days of a nuclear weapon explosion (fission bomb), or a nuclear accident like the one that happened in Chernobyl, the biggest source of radiation comes from the decay of the $$^{131}$$I isotope, which piles up in the thyroid. The product of its decay is the noble gas xenon:
$$_{53}^{131}I \to _{54}^{131}Xe+\beta^{-}+\bar{v}$$
• The $$^{137}$$Cs isotope is also able to get into the environment after nuclear weapon-experiments, or nuclear accidents. It causes contamination for 1-2 centuries, and it can build into the human body. It decays into barium:
$$_{55}^{137}Cs \to _{56}^{137}Ba+\beta^{-}+\bar{v}$$

In $$\beta^{+}$$-decay one of the protons in the nucleus transforms into a neutron, while it emits a positron ($$\beta^{+}$$ particle) and a neutrino (ν).

$$_Z^AX \to _{Z-1}^AY+\beta^{+}+v$$

This type of transformation can be observed in those isotopes that have proton-excess compared to the proton-neutron ratio of stable nuclei with the same mass-number. The atomic number decreases by 1.

Let's review some examples!

The following four isotopes are used in positron emission tomography (PET). This is a really precise medical diagnostic technology. These materials allow us to locate and precisely measure tumours, and also to track metabolic processes.

• a $$^{11}$$C transforms into boron:
$$_{6}^{11}C \to _{5}^{11}B+\beta^{+}+v$$
• a $$^{13}$$N transforms into carbon:
$$_{7}^{13}N \to _{6}^{13}C+\beta^{+}+v$$
• a $$^{15}$$O transforms into nitrogen:
$$_{8}^{15}O \to _{7}^{15}N+\beta^{+}+v$$
• a $$^{18}$$F transforms into oxygen:
$$_{9}^{18}F \to _{8}^{18}O+\beta^{+}+v$$

In $$\alpha$$-decay a particle, made of two protons and two neutrons, (($$alpha$$ particle, which is a He nucleus) is emitted from the nucleus.

$$_Z^AX \to _{Z-2}^{A-4}Y+\alpha$$

This type of transformation is typical of more complex isotopes with higher mass numbers. The atomic number decreases by 2, and the mass-number decreases by 4.

Let's review some examples!

The isotopes, mentioned below, are members of the naturally occurring "uranium-radium" decay chain.

• $$^{238}$$U the most common uranium isotope, makes up 99.28 % of the uranium in nature. It is not fissile, so we cannot use it for nuclear chain reaction in nuclear power plants. The product of its decay is thorium:
$$_{92}^{238}U \to _{90}^{234}Th+\alpha$$
• The $$^{234}$$U isotope is found in barely measurable quantities in nature. It is also not suitable for fission. It decays into thorium:
$$_{92}^{234}U \to _{90}^{230}Th+\alpha$$
• The $$^{226}$$Ra isotope, which was discovered by the Curie couple, transforms into radon:
$$_{88}^{226}Ra \to _{86}^{222}Rn+\alpha$$
• $$^{222}$$Rn is the most common radioactive isotope that can be found in the air around us (in ground floor rooms 40-60 decays per second per $$m^{3}$$. This radionuclide causes 51 % of the natural radiation exposure of the civilian population. This isotope decays into polonium:
$$_{86}^{222}Rn \to _{84}^{218}Po+\alpha$$

The decay of a nucleus (for any type of decay) is a random process. It cannot be influenced from the outside. The probability of transformation is specific to a given isotope. There are isotopes that are very short-lived, with a high probability of decaying (e.g. $$^{13}$$O), while it may take others (like $$^{238}$$U) millions of years to transform. Examining a large number of nuclei, it is meaningful to introduce the concept of half-life ($$T_{^1⁄_2}$$), which shows how long it takes for half of the atoms to decay with a good approximation. For a given type of decay and mass number, the chance of conversion is higher if there is a large difference between the initial nucleus and the product in terms of average binding energy per nucleon (the level difference is large in the 3D model); in this case the half-life is shorter. This quantity can be used to describe the time course of the transformations. The radioactive decay law gives the number of nuclei that remained undecayed from the original $$N_{0}$$ sample after time $$t$$:

$$N(t)=N_0*(\frac{1}{2})^\frac{t}{T_{^1/_2}}$$

The fission was first discovered by L. Meitner, O. Hahn and F. Strassmann in 1938.

 L Meitner O. Hahn

We can observe this phenomenon in the case of only a few isotopes (e.g. $$^{235}$$U, $$^{239}$$Pu). The nucleus captures a slow neutron (thermal-neutron) and it splits into two nuclei while new neutrons are created. The outcome of the fission is not obvious. The product-pairs are generated with differing probabilities.

A typical outcome of $$^{235}$$U fission:

$$_{92}^{235}U+n\to_{56}^{139}Ba+_{36}^{94}Kr+3n$$

There are isotopes that are capable of undergoing spontaneous fission (e.g. $$^{252}$$Cf, $$^{240}$$Pu), as well as those that can be fissioned by some external impact, such as neutron capture. Isotopes that can be fissioned by slow neutrons ($$^{235}$$U, $$^{239}$$Pu) deserve special attention, as they can be used to achieve a self-sustaining neutron chain reaction. The $$^{238}$$U isotope, on the other hand, can only be split by fast neutrons.

After the deceleration of the newly created neutrons, new fission reactions might begin. This is the nuclear chain reaction.

On the stability object, it is clearly visible, that the columns of the fission-products are lower than the uranium's column (closer to the "ideal iron"), which means that energy is released in the reaction. Part of the energy, which was "stored" in the initial nucleus, appears as the kinetic energy of the products. The rest of it appears in the form of electromagnetic radiation (gamma radiation). The kinetic energy transforms into heat, which causes warming in the matter. – It is important to note that it means a million times as much heat compared to what we can get from the burning of the same mass of coal.

The first experimental nuclear reactor was built with the leadership of E. Fermi in 1942.

E. Fermi

This reactor was only able to produce heat (with less than 2W power). It took a long time until they built the first electricity generating nuclear stations; they were mostly used for plutonium production for war purposes. The first reactor, which produced electricity for a power grid for the first time, was put into operation in the soviet Obninsk in 1954. It was followed by the Shippingport nuclear station in 1957, which was the first power plant to generate electricity for commercial use in the United States. Today, there are 440 working nuclear reactors in the world, in 30 different countries. These reactors cover 10-12 % of the energy-need of the world population. Currently, there are 70-80 new reactors in the designing and building process. The great advantage of nuclear power plants compared to "conventional" power plants (coal, oil, gas), is the lack of CO2 emission, so they don't contribute to global climate change. The military use of nuclear fission was the nuclear bomb, which’s development was finished in 1945. The sad truth is that the energy coming from the heart of the matter is capable of huge destruction. The bombings of Japan, the nuclear weapon-experiments and the nuclear disasters of Chernobyl and Fukushima must be lessons for our civilization.

Nuclear fusion was first described by H. Bethe in 1939.

H. Bethe

The main concept of this phenomenon is that nuclei with quite low mass numbers unite, while energy is released in the process. The explanation for this is easily understandable with our 3D model: near hydrogen nuclei become more stable with the merge as they get to a lower energy state from an especially high energy state. Thus, the nucleons are more strongly bound in the new state and the newly formed nucleus is more stable. Due to this "great fall", which is visible on the stability object, more energy is released than ever mentioned in the above.

Six fusion examples:
1. $$_1^1H+_1^1H\to_1^2H$$ (+1,44MeV, 0,23 pJ)
2. $$_1^1H+_1^2H\to_2^3He$$ (+5,49 MeV, 0,88 pJ)
3. $$_2^3He+_2^3He\to_2^4He+2_1^1H$$ (+12,86 MeV, 2,06 pJ)
4. $$_1^2H+_1^2H\to_2^3He+n$$ (+3,25 MeV, 0,52 pJ)
5. $$_1^2H+_1^3H\to_2^4He+n$$ (+17,6 MeV, 2,82 pJ)
6. $$_1^2H+_2^3He\to_2^4He+n$$ (+18,3 MeV, 2,93 pJ)

For comparison: during the oxidation of a carbon atom, in the $$C + O_2 \to CO_2$$ process, the energy release is 29,25 eV = 4,68 aJ. So in the case of equal initial masses, a million times more energy is released from fusion.

For fusion to occur, very high temperature (about 100 million K) plasma-state matter is required. This process provides the energy generation of stars. That's how the Sun gives its life-giving energy to Earth.

Note that the direct result of process (1) (with 0.42 MeV energy release) is a $$^2$$H- ion and a positron e$$^+$$. The latter annihilates almost immediately with an electron, resulting in the formation of two gamma photons with a total energy of 1.02 MeV. In stars, mostly the fusion reaction chain (1)-(3), which starts with the lightest isotope of hydrogen ($$^1$$H), produces the energy. Processes like (4)-(6) are very unlikely and therefore unfeasible on Earth. The huge amount of matter in the stars and the enormous gravity that holds it together even at high temperatures allow the reaction chain (4) - (6) to take place.

The first hydrogen-bomb test was in 1952. This is an even more devastating weapon than a "traditional" nuclear bomb. (Just 400 years before, the defenders of Eger Castle repelled sultan Suleiman's army. The development in military technology is astounding...)

Fusion might be the energy source of the future. Scientists have been working on the development of the fusion reactor since the middle of the twentieth century. This would be an absolutely environmentally friendly solution to the energy need of the growing population, and we have a virtually unlimited amount of fuel for it. A functioning prototype might be available in a decade. However, we will have to wait at least until 2050 for a “mass producible” implementation, according to scientists. - Releasing the energy, stored in the nuclei, is a huge responsibility. Real scientists and engineers do not develop weapons, but are building the bright future of humanity!