Americium

While the general public get both excited and concerned about plutonium, some of the other actinides are equally important. Americium because of its higher stability of the +3 oxidation state has chemistry which is very different to plutonium.

I have seen predictions which suggest that the americium-241 either released from Chernobyl or formed in the environment as a result of the beta decay of the plutonium-241 released by the accident will become the radionuclide of greatest importance near Chernobyl after the cesium-137 has decayed away.

Fukushima will be a different matter as far less of the americium or plutonium in the fuel was released during the accident.

The age of the earth and where I have been

Dear Reader,

I suspect that some of my regular readers have noticed that I have not been blogging for a while. The reason why I have stopped blogging for a while is that I am in the process of writing a book. I saw something on UK TV today which is an outrage, it is the idea that the earth is only about 6000 years old.

Now while freedom of thought and speech allows people to hold and express what ever ideas they have, even the outlandish and odd ones ! But the idea that the earth is only 6000 years old is deeply disturbing and clearly wrong !

I heard one of the young earth creationists being told by a geoscientist about radioactive dating of rocks and minerals. The creationist said something to the effect of “how do you know when the clock was zeroed”. I know that in Africa many years ago a natural nuclear reactor operated. Some of the fission products such as Tc-99 have decayed away. This suggests that far more than 6000 years has passed since the reactors were in operation.

I will leave it up to my readers to look up the half life for Tc-99 and work out how long it will take for 90 % of the Tc-99 to decay to Ru-99. Think of it as homework.

Cesium chemistry in Japanese soils

Dear Reader,

After having spent much of sunday in a fruitless search for a storage box for my garden tools, I get the chance to write to my beloved readers another blog entry. Now all along I had been making the prediction that the cesium would stick like glue to the soil and stay in the top layer. Some workers have examined soil samples and in a paper (Takeshi Fujiwara, Takumi Saito, Yusa Muroya, Hiroyuki Sawahata, Yuji Yamashita, Shinya Nagasaki, Koji Okamoto, Hiroyuki Takahashi, Mitsuru Uesaka, Yosuke Katsumura and Satoru Tanaka, Journal of Environmental Radioactivity, 2012, 113, 37-44) an examination of soil samples from the Fukushima area has been reported. In this paper it has been shown that the cesium is concentrated in the top layer of the soil.

Circa 70 % of the cesium is in the top 2 cm in the soil, while the iodine was more mobile. The good news is that the cesium will not enter ground water, further good news is that plants with deep root systems are unlikely to absorb much cesium. The bad news is that the cesium will be in the right part of the soil to enter grass via its shallow roots and the fact that the cesium is in the upper layers of the soil will increase the external threat due to gamma photons.

It is interesting to note that the Japanese may not worked out a sensible way to store the contaminated soil which is removed during the clean up of land. It has been reported that people are being required to store contaminated soil from cleaning up their own gardens on their own land. I think it would be better if industrial estates were used as places to store the contaminated soil while the government find a place to store the soil for the next 300 years.

I have spoken to my legal advisor about human rights, and my advisor told me that the right to have a safe environment could override the right to object to a waste store in a given town. I hold the view that if the waste stores are sited well away from homes and other places where the general public spend a lot of time, then it is OK to raise the dose rate in the waste store. The waste store should be designed to avoid releasing cesium into the environment and the construction of the waste store should be done in such a way that it does not increase the dose rate at the edge of the site. I think that the reference dose rate for the latter point should be the dose rate at the edge of the site before the clean up is done.

If the dose rate at the edge of the site is 2 microSv per hour, then this will give a person a dose per year of 17.5 mSv which is a big dose for the general public. But if the dose rate at the same spot was 2 microSv per hour before the clean up which generated the waste which will go into the store is conducted then the clean up will have a neutral effect at the edge of the waste store but will have a good effect on the majority of the land.

I may do some calculations on the subject if I get time in the near future.

Muons and Fukushima

Dear Reader,

One of the great problems right now is working out where the fuel in the damaged cores and the ponds is, and in what condition the fuel is in. We can take for granted that the fuel which was in units 1, 2 and 3 has been damaged by overheating. But the state of the fuel in the ponds was a bit more of a mystery to us.

After clearing the rubbish out of the pond at unit three it has been possible to inspect the pond, the pond is frankly in a bit of a mess. But the fuel seems to have escaped serious damage. Photographs have been taken of the fuel racks in the pond and it does not look like there has been been any dire melting or explosions in the pond.

I have seen that some samples have been taken from the pond at unit four to allow them to be examined (these were samples of unused fuel which were being stored in the pond at the time of the accident). The work so far suggests that the fuel in the pond is in good condition. This suggests strongly that no nuclear explosion occurred in the pond.

The other great question is the state of the reactors. I saw something interesting recently, it is a sensing system based on cosmic rays (muons). This looks to me like a good method for finding the fuel inside the damaged reactors without having to get up close and personal with the stricken reactors.

Another thing which needs to be done is for society to recover from the accident, I have seen some advice from the IAEA on the subject of remediation of the contaminated land (outside the nuclear reactor park). This document might be of interest to some of my readers. It includes a discussion of the cleaning of different types of areas which include farmland. As I predicted it does include the question of deep ploughing the land.

Palomares and the H-bombs

Dear Reader,

Now some doomsayers may have tried to tell you that once radioactivity appears in soil that you should give up all hope, also on the otherhand some false prophets of insincere reassurance will just tell you to stop worrying and that “everything will be OK”. My advice is not to trust either of these two false friends.

The story of the air crash which involved four H-bombs has popped up again, the BBC report that the local people in Spain are fifty years after the air crash unhappy about what has been done.

The BBC report suggests that the local farmers have a problem getting a good price for their produce at market. I would like to point something out.

The plutonium in the H-bombs would have been in the form of the metal, during the accident this would have been burnt into plutonium dioxide. Now the thing to note about plutonium dioxide is that it is very hard to dissolve in acid, also it is not mobile in soil. Any plutonium which was in a water soluble form is likely to have bonded to the soil minerals thus making it impossible for plants to absorb it via their roots.

M.I. Sheppard and D.H. Thibault, Health Physics, 1990, 59, 471 to 482 gives the binding constants for most metals to the four common soil types. It lists for plutonium the following Kd values.

Sand, 150 L/kg

Loam, 1200 L/kg

Clay, 5100 L/kg

Organic, 1900 L/kg

This means in a bucket containing a mixture of clay type soil and water that the plutonium content of the soil (Bq per kilo) will be 5100 times higher than the plutonium content of the water (Bq per litre).

Hence when 1000 Bq of plutonium is added to a litre of water mixed with a kilo of clay type soil, then the soil will absorb 999.8 Bq of plutonium while 0.2 Bq of plutonium will stay in the water. This calculation is for a static batchwise experiment but it will help experts in the field make predictions about the mobility of plutonium solutions in soil.

Another good bit of news is the fact any plutonium dioxide in the dust will not be well absorbed if it is swallowed (dust on the surface of the food), so orally the plutonium dioxide is not a great threat to life and limb. If you were to swallow a well sintered particle of plutonium dioxide it will pass unchanged through your digestive system.

However plutonium dioxide in the lungs is very dangerous to a persons health, I think that a key thing to do in Spain is to keep the plutonium in the most contaminated soils from entering the air as a dust. I think that the ban on building, farming or walking in the contaminated area is a good idea. But I think that it might be a good idea to pour concrete or asphalt onto the worst hot spots to try to fix the soil to keep it from becoming mobile again.

One of the problems with plutonium is that the colloidal particles of clay can make the plutonium mobile, while the plutonium does not move freely through the soil in aqueous solution the colloidal particles can move through the cracks in the soil. Thus sealing the soil would help to stop the plutonium from reaching the surface again in the form of dust.

BNCT a great way to cure cancer

Dear Reader,

Recently I looked into the core of a nuclear reactor for the first time in my life, the closest I had been before then was looking through the door in the inner shielding at the top cap of a defunct reactor which had been shut down decades ago.

I was standing in the operating position above the water pool of a 250 kW reactor which is used for research, training and for treating cancer; the reactor was not running while I was visiting. Apparently in that location the dose rate is about 400 microsievert per hour when the reactor is running, while this dose rate is no where near the level which would cause an injury or death. As the 1970s LD₅₀ dose for radiation was about 3.5 grays, it would take 8750 hours there to reach this dose. The 365 days required to get this dose would mean that the self repair mechanisms in my body would reduce the baneful effect on my body. I do not think that it would make me fall down dead, but within a week or so I would be hitting my yearly limit, so that I would not want to linger in that spot while the reactor is running.

It was an interesting view looking down through a 6 meter pool of water at the core of the reactor; this reactor is a type which is not designed to make electric power. Instead it is designed to make neutrons for radioisotope production, for training and for the treatment of cancer. Almost twenty years ago the reactor was modified to allow it to be used as a neutron source for the treatment of cancer by the boron capture method.

Now I know that some elements in society are very antinuclear but I would ask even the most antinuclear people to stop, read this and think for a while. Frankly I would like it if you shared my point of view but even if you do not come away from reading this with my point of view I accept that people are free to choose what they like to believe.

Now if you have the misfortune to get cancer then one of the treatment methods is radiation, now the problem is that it is best to give the cancer cells one heck of a going over with one almighty dose of radiation while only giving the healthy tissue a very small dose. This is the ideal but sadly with many radiation treatments it is not quite possible to do this.

The most common method seems to be either X-rays or gamma rays delivered from a source outside the patient. The problem with these treatments is that the beam of radiation damages all tissue that it passes through. One solution to try to spare the healthy tissue is to aim beams of radiation into the person from different angles so that the paths of all the different directions converge on the spot where the nasty tumour is. This is not a perfect way of doing things, no matter how good the radiation expert is they will damage some healthy tissue.

The next step up in controlled and localised dose is to implant a source into the person; it is possible to implant a small but intensely radioactive source right at the spot where the cancer is. This can be used to treat a range of different cancers which include cancer of the cervix, breast and prostate. As radiation obeys an inverse square law this treatment is often very good at sparing the healthy tissues.

If you double the distance from the source you make the dose four times lower, while if you triple the distance from the source then the dose is nine times smaller. I hope that you can now see that the effect should be very well localised in one part of the body. With the right choice of photon and beta particle energy you can make the dose even shorter ranged thus allowing you to wipe the smile off the cancer’s ugly face, send it away with its tail between its legs while leaving the vast majority of the person undamaged.

Sounds great doesn’t it! But there is a fly in the ointment. Today for some applications some of the greens are yelling that we need to stop using nuclear reactors. The problem is that for the generation of the radioactive sources often the only thing which will do the job is a nuclear reactor which has been optimised for a high neutron flux. To do this you need to make the core nice and compact and run the reactor with a highly enriched fuel. Here is one of the best arguments for keeping radioisotope production reactors, while they might not fit in with some people’s idea of what is green they do provide an affordable and reliable supply of lifesaving diagnostic and curative medical products.

Now some people might be yelling at the screen that we should ditch the old fashioned radioactive sources for medical use and use modern particle accelerators like LINACs. I would like to point out that the treatment systems based on radioactive sources are simpler and there is much less to go wrong. Using no more than a sheet of graph paper it is possible to predict the strength of a radioactive source on day X, while accelerators are more complex. I am aware of radiotherapy accidents in both Poland and the USA where accelerators have failed to behave as expected. Both cases caused some ugly overexposures of people.

Also to deliver the radiation just where it is needed to some where like the cervix or the prostrate it is not possible to do it with a typical medical accelerator. The way that the LINACs typically work is by whipping up electrons to very high speeds and then slamming them into a metal target. The change in velocity (deceleration) of the electrons cause them to emit very high energy gamma rays. An alternative second method is to use a gadget called a betatron. Both the betatron and the LINAC are suitable as replacements for the cobalt-60 based teletheraphy units which used radioactive sources to make beams of gamma rays, but they are not able to replace the treatments based on radioactive sources which are placed right in the tumours.

Now while brachytherapy is all very well, there is something even better. One of the problems with cancer is the oxygen effect. If tissue is nice and well oxygenated then low LET radiation like gamma and X-rays are good at causing harm. But when the tissue is poorly oxygenated then it has much less effect. While the surface layers of a tumour are often well oxygenated, the core of a tumour is often poorly oxygenated. What can happen is that when a tumour is given a dose of radiation the inner less oxygenated cells survive and then continue to grow thus making the tumour reappear.

But a high LET radiation such as alpha particles still works even if the oxygen content of the tissue is low. If boron is subjected to neutron bombardment then it forms alpha particles which are able to then do immense damage to the cancer while leaving the healthy tissue alone. The reason that this works is that the person is given a dose of a boron containing drug which mainly absorbs into the cancer cells. The drug used in Finland for this treatment is L-para-Boronophenylalanine, this is an amino acid bearing a B(OH)₂ group.

The boron-10 reacts with the neutrons to form alpha particles and lithium-7.

¹⁰B + n → ⁴He + ⁵Li

The helium and lithium-7 ions then damage the cancer cells, as the boron concentration in the healthy cells are low the healthy tissue gets a far lower dose. Here is a picture of the boron compound which is used for the treatment.

A molecule of the amino acid which bears the B(OH)2 group required for the BNCT

Now some of those of you reading this blog might not be the greatest enthusiasts of the nuclear sector, but I would like to caution the “antinuclear brigade” against throwing the baby out with the bath water.

While I am well aware that it is possible to make bombs using some nuclear technology, I would like to point out that Patrick Moore pointed out that the fact that car bombs made with ANFO (Ammonium Nitrate Fuel Oil) are bad. Frankly I have to say I strongly agree that ANFO based car bombs are perfectly horrible.

But he wrote that the fact that you can make a nasty large bomb out of a car, some ammonium nitrate fertilizer and some diesel fuel is not a good reason to ban any of these three items.

I would like to also point out that the nuclear equipment in the form of a radiotherapy reactor is not in a form which is suitable for use as a weapon, I think that the only weapon I had access to at the reactor site were some lead bricks in the radiochemical lab and the bright yellow extra long tongs. I think I can get some weapons which are more suitable for mindless violence from a typical garden centre !

I have to explain something to you, it is possible to use many objects as weapons but the fact that it is possible to employ or adapt an object into a weapon is never a valid reason for banning an object. I will give you an example, in Mr Archer’s prison diary it explains how one person once took a toilet brush, they cut off the bristles and then sharpened it into a sword. The fact that someone managed to adapt a toilet brush into a sword should not be used as an excuse to ban the things !

Bob and his nuclear “facts”

Dear Reader,

It has come to my attention that a person calling themselves Bob Nichols is publishing “news” on a web site. Being a person with some knowledge and understanding of nuclear matters I thought I would take a look.

Bob as we will call him is making the bold claim that nothing is being done to mitigate the accident or clean up the site. I think that this claim is totally false, I am well aware that waste water on site is being contained, treated and then reused to greatly reduce the amount of radioactivity which is released into the ground and the sea.

Bob has claimed that even industrial robots can not cope with the radiation levels on site, I think that this is deeply wrong. A friend of mine has been on the site and he only got a small dose. I would like to know what location he is talking about. In a normal nuclear plant there are some areas which are off limits to humans for radiation safety reasons during normal operation. After shut down it is possible to enter some of these areas within minutes. There are areas at the Fukushima site (inside the reactor pressure vessels and in some areas of the containments) which might be off limits for humans for many years but I suspect that the vast majority of the plant buildings can be entered by either humans or robots.

He suggests putting the reactor cores under water, this is being done but as some of the reactors have leaks it is not a simple matter. His text suggests that no work has been done to fix the reactors is misleading, while fixing these reactors is not a simple matter the work to fix the site has already started.

He writes about the “evils of uranium”, but I would like to point out that small uranium particles are unlikely to stay in the human body for long. Uranium oxides tend to dissolve in water when oxygen and carbon dioxide are present. The uranium will then be lost via the urine. If he wants to think about any radioisotopes then he should be thinking of the shorter lived beta/gamma fission products which were released back in march 2011.

He also fails to note that the amount of radioactivity in the reactor site is now far less than it was back in march 2011, radioactivity in a nuclear reactor’s fuel tends to decay away greatly after the plant is shut down. He also makes some rather far fetched claims about chernobyl claiming that 30 % of the core was released, trust me only about 3.5 % of the fuel at Chernobyl was able to leave the plant. If Bob had read either an undergraduate text book on nuclear chemistry (I can name two books which would tell him this) or even (dare I saw it) wikipedia then he would have found that the release of radioactivity from a damaged nuclear plant is controlled by the boiling point of the main form of the element.

While iodine, tellurium and cesium are mobile, the real nasties such as plutonium and strontium are much less mobile (thank goodness for small mercies). His suggestion of using atomic bombs to cause a landslide to make the reactor site fall into the sea is very silly. I sincerely hope that nobody ever tries to do this !

The right to roam into a nuclear site ?

Dear Reader,

It has come to my attention that some tourists have been indulging in some outdoor activities which sadly have got them into trouble. Now for those of you who have not lived in Sweden, I need to tell you about the general right to go anywhere in the country side. Unlike the UK any person in Sweden can go for a walk anywhere in the country side, this is known as allemansrätten which even gives you the right to take wild fruit from land which you do not own.

However the allemansrätten is not a license to do as you like in the country side, for example I can not pitch my tent in next door’s garden. One of the key ideas behind the way in which people in Sweden behave when using the allemansrätten rights is the idea that you should not damage anything or disrupt the lawful activities of the landowner or another person. For example I should not trample over a field of wheat and disrupt the farmer’s crop growing by walking all over his/her plants.

I would also like to point out that some sites are restricted places which the allemansrätten does not apply to, for example the vault at a bank is not a place I can just stroll in and out of, also the King’s palace is a place which is restricted and also nuclear sites are restricted. A less grand place which is also restricted is next door’s kitchen, the allemansrätten does not allow me to gather frozen berries from their freezer, nor does it allow me to go rock climbing on their roof.

I have read that some of these nature walkers have been using ladders to bypass some fences at a outdoor leisure site in the east of Sweden, sadly they choose the wrong site. I also note that a simple ladder does not give you a good view of nature or a very challenging climb. I would like to respectfully suggest in future that these nature walkers sign up for a session of via ferrata, rock climbing or perhaps they should just go hill walking in the lake district.

The ladder is too easy a thing to climb and it is unlikely to give a person much of a feeling of satisfaction, I suggest that a tree, climbing wall or rockface would be better.

While doing via ferrata, rock climbing or hill walking does provide you with a very enjoyable view, sadly going over the fence at Forsmark park does attract the attentions of the boys in blue. I have heard that the climbers are to appear before the beak to explain themselves. I think that their deeds are somewhat more serious than sneaking onto a via ferrata route without paying. I have to agree with the sentiment expressed at “Nuclear Power yes Please” that the best way to visit this park is to phone up and ask them to let you in via the front door rather than risking damaging your clothing while climbing the fence.

I would be interested to know what these nature walkers have done with their ladders after their trip to the park, I could always do with an extra ladder for working on fruit trees or the side of my house.

Another group of nature walkers have also misunderstood the allemansrätten rules at a park south of Sweden, this park is a seaside site which commands impressive views of the sea. Here the nature walkers were using metal work tools on the fence. I think that they have very much misunderstood the right and wrong place to do some recreational metal work. If you want to do some modern art using metal work tools or some other recreational metal work, I suggest that you buy metal work tools from the wonderful choice at the Swedish hardware shops and the go home and try some amateur blacksmithing or for those with a more down to earth point of view then perhaps you could do some DIY home repairs or improvements.

On a more serious note, I would like to know if the Greenpeace people are trying to commit “suicide by cop”. The core thesis in the “suicide by cop” is that a person does something which causes a police officer (or another person) to fear for his life (or the lives of others) then the police officer then uses deadly force to stop the person. Thus the person (who was unable or unwilling to kill themselves) gets to commit suicide by proxy. I think it is only a matter of time before a greenpeace activist is seriously injured or killed during an illegal entry into a nuclear site, I think it is time for greenpeace to call time on this irresponsible behaviour.

Now those of you who are greenpeace members or even activists who are reading this, I have something to say to you. I care for the environment, but I insist on truth and responsibility. While some of what greenpeace has done (like saving the whales) I strongly agree with, the antinuclear campaigning (and the antichlorine campaign) are the height of folly. To my mind they are both examples of eclipses of reason, in both cases the credibility of the green movement in my mind has been dragged through the mud by no one other than the Green movement themselves.

In the case of chlorine, I freely admit that there are some very horrible chemicals which have chlorine in them but on the other hand their are some substances with chlorine in which are benign and very important for our health. Greenpeace fell into one of the most basic traps documented in the book straight and crooked thinking, of confusing some with all. For an organisation who are claiming to be given out advice based on science and reason they should be deeply ashamed of that episode. The current antinuclear campaigns seem to be the product of the same type of bad thinking.

Alpha decay part II

Dear Reader,

As I sit typing in a railway carriage on the way home sitting near a young lady who is sporting a ”Nuclear power no thanks” badge, I sit here thinking about nuclear processes hopeful that the young lady does not notice what I am typing.

It is interesting to note that one of the physical effects which regulate the reactions which go on inside the red sun of the “Karnkraft nej tak” badge are the electrostatic forces which oppose fusion. The same forces have an effect on the reverse reactions (alpha emission, fission and all the cluster emissions which come between those two extremes).

Now since I had a rather short hair cut recently I can not demonstrate electrostatic attraction using a comb dragged through my hair. I will let you try that at home, also I do not have a cat to rub on a bit of plastic so I can not use that either.

But back to nuclear processes and electrostatics, to a first approximation the atomic nucleus can be treated as a charged sphere. The size is given by the following equation.

R = R_o (A)^0.3333

Where R_o is equal to 1.2 x 10^-15 m, while A is the total number of nucleons (the sum of the number of protons and neutrons) in the nucleus.

So radius of a plutonium-238 nucleus is 7.44 fm, while its daughter (uranium-234) has a nuclear radius of 7.39 fm while an alpha particle has a radius of 1.90 fm. Using these radii we can calculate the energy required to push the alpha particles from plutonium-238 back inside the nucleus.

To do this we need a few more equations from A-level physics.

As the capacitance of a sphere is given by

C = 4 π ε r

Where ε is equal to the permittivity of free space which is 8.854187817620 × 10⁻¹² F m⁻¹ or just 8.85 × 10⁻¹² F m⁻¹

We can use this to estimate the electrostatic energy required to hold an alpha particle on the surface of the uranium-234 nucleus. As soon as the alpha particle is taken out of the nucleus it is no longer being strongly bonded by the very short ranged but very strong attraction between the protons and neutrons in the nucleus (the strong force). So suddenly only the electrostatic forces apply to the system (the weak force and gravity are far far weaker)

This energy (28.5 MeV) is far greater than the decay energy of the plutonium-238 (5.593 MeV), as a result the alpha particle, what has to happen is that the alpha particle must overcome this energy barrier before it can leave the nucleus of the atom. What happens is that by quantum tunneling the alpha particle leaves the nucleus of the atom and then goes on its merry way. Here is a graph of the electrostatic energy in MeV vs the distance from the centre of the nucleus for both the alpha particle and the carbon-12 nucleus.

Electrostatic energy as a function of distance from the centre of the daughter nucleus

When the calculation is repeated for the loss of a carbon-12 nucleus from plutonium-238 to form radium-226 then I have estimated that the energy barrier is 74.5 MeV, while the decay energy is now higher at 22.5 MeV you now have a bigger barrier and some other things also help slow down the release of C-12 nuclei.

I hope to get onto these things later.

Why does alpha decay occur

Dear Reader,

I bemoan the fact that few text books explain why things happen, many text books are content to tell you what happens when they discuss radioactivity but are not able to or willing to explain how it happens. Now some time ago I explained the driving force behind beta decay, today we are going to start to deal with alpha decay.

Alpha decay is when the nucleus of an atom emits the nucleus of a helium-4 atom, now I am sure that some of the smarter readers will have asked (or be considering) the question of why is it always a helium-4 nucleus. Now I have to tell you that helium-4 has a special high stability.

I know as human beings we like to think of ourselves as more than just the sum total of our parts, while one recent estimate suggests that a human body is only worth $ 4.50 the EPA think that a human life is worth $ 9100000. I do not want to get into a debate about the morals or value of human life but it is clear that if we use the EPA estimate that a human is worth much more than the scrap value of the typical human body.

In the same way a group of neutrons and protons which make up an atomic nucleus has a mass which is often different to the sum of the mass of the free nucleons. This is because when they bind to each other some energy is lost. because energy and mass can be interconverted (E = mc2) this means that the mass is changed slightly. In general the more strongly the particles are bonded to each other the lower the energy of the nucleus and the lower the mass is. Now carbon-12 is used as the zero point for many things, the mole is defined as 12 grams of carbon-12 and also it is used as a zero point these nuclear calculations.

If we look at a graph of the excess energy which is due to the extra mass which is associated with taking protons and neutrons out of a very stable system into a less stable system divided by the number of nucleons in the nucleus against the mass of the nucleus then we get a funny looking graph. It has a general downward trend over the mass range 1 to 30 but there are some masses which are extra stable. For this graph I have used the stable nuclides (stable isotopes) except for two points which we will get onto later.

These are 4, 8, 12, 16, 20 and 24 which are magic numbers. It is important to note that these nuclei have even numbers of protons and neutrons. We will get onto magic numbers again some time in the future. Here is the graph below.

A graph of excess energy (keV) per nucleon against the mass of the nucleus

Now I hope that we should be able to see that the helium-4 nucleus is a very stable small fragment. We will continue soon with alpha decay, but before I go you might find this link useful. It is for some lectures on the nuclear physics of radioactive decay.