The Precarious Evolution of
the Atom Bomb

Despite the ongoing fascination, funding and fear towards Nuclear weapons that is ever present in the world today, they have only ever been used twice in conflict. Both times by the United States, both times in World War Two and both times dropped on Japan.  The resulting devastation in the cities of Hiroshima and Nagasaki are thought to have brought an end to the Second World War. But what kind of ungodly science could cause over 200,000 casualties over a space of three days? The answer is unerringly simple, and one that might strap you back into your year 9 school shoes and back into period 5 science. However, an understanding of this science will do more than just help you notch a few more points when University Challenge is playing on your TV. It will give you the context of the respect and exclusivity that these weapons have today (with only 6 countries obtaining them), whilst allowing you to recognise that the science behind these nuclear weapons is a good thing for humanity, despite the risk of the devastating consequences of a nuclear war.

The physics of fission and fusion

The atomic bombs dropped in World War 2 were fundamentally exploded using a process called nuclear fission. To put it simply, the explosion is the energy released by the splitting of the nucleus of an atom (the dense part of the atom, where all the protons and neutrons live).

When a single free neutron strikes the nucleus of an atom of radioactive material like Uranium, it knocks three more neutrons free. Energy is released when those neutrons split off from the nucleus, and the newly released neutrons strike other Uranium or Plutonium nuclei, splitting them in the same way, releasing more energy and more neutrons. The U-235 atom then turns into a U-236 atom after impact from the neutron. The isotope, U-236 is unstable, and hence splits into fragments, which in this case are Kr-92 and 141-Br, as well as three more neutrons. This sparks a chain reaction almost instantaneously, which is why the size of the explosion is so big. The fission reaction that occurs in most fission bombs is shown below.

The fission equation (right) and a fission chain reaction (left) 

The total mass before fission is greater than the mass after (the waves correspond to enrgy in the form of light radiation, heat and sound)
The total 'Rest mass energy' is conserved after fission

I am sure you are all very familiar with Einstein’s famous equation E = mc2 but I feel not as many people understand its consequences towards nuclear energy. Without this equation, there would be no Little boy or Fat Man. The E in this equation stands for the energy difference in the masses of all the components, before and after the fission process. If the mass (m) of all the components of protons and neutrons is greater before the fission than after it, then energy must have been released. Einstein’s equation tells us that the conversion of mass into energy can occur. In fact, mass is energy. Mass is just energy that is at rest. Any mass (m) that is at rest, possesses mc2 of rest energy, which can be potentially available for conversion into other forms of energy. The lost mass of the fission fragments, in this case, is converted into other forms of energy. In the case of an atomic bomb, energy is given to photons which we see as light or feel as heat. Even though the masses are different, the total rest mass energy of the Uranium contents is the same as all the fission fragments and the photons that were released after ignition, and we can see this from the diagrams above.

The c2 in the equations is a huge number, and corresponds to the (speed of light)2 and this means that over 9 x 1016 more energy is released than mass is lost. That’s 9 with sixteen zeros behind it. This illustrates how such large amounts of energy are released in these explosions and why, despite containing only 64kg of bomb fuel (equivalent to the average mass of a person), Little Boy exploded with the equivalent energy of 16 Kilotons of TNT. In fact, if you were going to convert all the mass of your phone into energy, it would be over 210,000 times more powerful than the explosion of Little Boy (1). 

Einstein proved this formula in his paper: "Does the inertia of a body depend upon its energy contents'; published in 1905 (2)

What is important to realise, however, is that although c2 is very big, for each fission, the mass ‘lost’ is extremely small. The mass of a Uranium-235 nucleus is around 3.9  10-25 kg, and only 0.1% of this mass is converted to energy (3). This is why a chain reaction needs to occur. There needs to be enough fissile material for a chain reaction to occur, and this minimum mass is called the critical mass. 

Fusion, on the other hand, is where two elements have enough kinetic energy to overcome to force of repulsion from the strong nuclear force and bind together to form a new element. Since the force of repulsion is so strong at close ranges, the temperature required for fusion to occur must be incredibly high. When fusion releases energy, the two atoms before the reaction have more mass than the new element that is formed when the particles are bounded.

U-235 fission reaction
Fusion
Fusion reaction of H-3 (a Hydrogen isotope)

The graph below looks alarming and wretched; however, it perfectly explains whether fusion of fission will release energy. From early age intuition, we have been told that opposites attract, and this is certainly true in science. However, in the nucleus, this rule is broken, and protons (which have positive charge) are bounded to other protons and neutrons. These protons would normally repel each other, since they have the same electro-static charge, so there must be some energy that is keeping these particles bound. This is the binding energy. As you can see, the Uranium 235 (U-235) will have less binding energy than the two components that are released during fission (Kr-92 and Br-141). This means, that in order for the new atoms of Kr-92 and Br-141 to be formed, mass must be converted into energy in order for there to be sufficient binding energy for these nucleus’s to be bound.

However, fusion works for lighter elements. Look at the bottom left of the diagram, we can see that hydrogen (H-2) has a much smaller binding energy per nucleon than Lithium does. Therefore, if Hydrogen nucleus’s fuse tighter to form Lithium, mass will be converted into binding energy, and hence a massive explosion will ensue. This is because the mass of three H-2 atoms is more than the mass of one L-6 atom, even though they contain the same number of protons. This graph also shows us that fusing hydrogen together produces more energy than fission does per unit mass. The difference between the binding energy of H-2 and L-6 is around 6 times greater than that binding energy difference from the fissile products of U-235. We can see this from the steep line from H-2 to L-6, and the gentler line from U-235 to Cd-110 for instance. If you don’t take my word that fusion converts more mass into energy than fission does, then consider that the sun (the glaring ball of fire that will blind you if you look at it despite it being over 148 million km away) is powered by fusion in its core.

Graph of binding energy per nucleon

The Manhatten Project

The programme of the development of Nuclear bombs was one of the key components in the acceleration of modern-day science. The Manhattan Project, which was the US’s programme into the advancement of nuclear weapons, injected around $2 billion (worth around $23 billion when adjusted with inflation) into areas such as fission research, the enrichment of uranium, bomb testing as allowing the best nuclear scientists in the world to collaborate together on the project (4).

An important discovery of the Manhattan Project, was the realisation that a bomb containing Plutonium (opposed to Uranium) would not explode correctly if the chain reaction was started when a single neutron was fired into the fissile material. The idea of a neutron in gun is shown in the chain reaction diagrams and explains fission simply. However, in 1943, a test on the ‘thin man’ neutron gun found that plutonium-239 predetonated using this method, the bomb exploded too early (meaning the pilot could not escape), and not enough reaction occurred before the whole bomb exploded, so not enough energy was released. Instead, a method known as implosion was developed, led by scientists such as Seth Niedermeyer. Implosion removed the neutron gun and instead used explosives to crush a subcritical sphere of fissile material into a suitably smaller and hence denser form. Since the atoms in the fissile material are now packed more closely together, the neutron capture rate increases and the mass becomes a critical mass, meaning the explosion occurs. This ensured that the explosion could be denoted at an appropriate time (5).

Test bombs were exploded in early 1945. The code name for the first bomb was Trinity, and the bomb was nicknamed ‘gadget’. Gadget was held up 400m high in the air by a tower and then detonated on the 16th July 1945. The explosion was so immense, that it left a 76m wide crater filled with radioactive glass. A shockwave was felt over 100 miles away and the explosion was heard in El Paso Texas. So protected was the secrecy of the Manhattan project, that the General in charge had to issue a cover story, blaming the sound on an ammunition magazine explosion at a nearby military field. It is suggested that no more than a dozen people truly understood the full meaning of the Manhattan project, despite over 129,000 being employed in various Manhatten test sites across the country (6). Morale was often so poor between workers (since many were working like ‘moles in the dark‘, with no clue what they were creating) that Manhattan sports leagues were created, hosting over 10 football and 21 baseball teams (7).

Startlingly, Edward Teller was commissioned to write a report called “Ignition of the Atmosphere With Nuclear Bombs.” to investigate whether a fission bomb could cause the atmosphere to ignite. There was a fear that the extreme heat induced by the bomb would be hot enough for  the hydrogen atoms in the air and water to fuse together, and cause a runaway fusion chain reaction in the atmosphere. This more evidence on how much of a continental shift in weaponry the development of the atomic bomb prompted; scientists were now worried about the destruction of the world from what they had created (8).

Little Boy (above) was a Uranium fuelled neutron gun-type atom bomb

Fat Man (above) was a Plutonium fuelled implosion type atomic bomb

 

 

If the radiance of a thousand suns were to burst at once into the sky, that would be like the splendor of the mighty one”

Robbert Oppenheimer (a chief scientist behind the project, seen right) quoting from the Bhagavad Gita (a Hindu holy text) whilst observing the Trinity test explosion

Impact on the War

The immediate impact on the dropping of the atomic bombs on Hiroshima and Nagasaki was the surrender of the Japanese Empire to the allied command forces on August 15th 1945. This can be shown since, after the first atomic detonation of the 6th of August, Harry S. Trueman (the American president at the time) called again for Japans surrender, warning them that if they refused they should “expect a rain of ruin from the air, the like of which has never been seen on this Earth”. It is believed that the Japanese did not immediately surrender here, because Japanese Generals such as Admiral Soemu Toyoda argued that the US could not have any more in supply. However, the second bomb dropped on Nagasaki signalled to the Japanese Emperor that not only was the war lost, but that the Japanese race could face total destruction, and hence he subsequently surrendered. The Japanese’s refusal to surrender earlier in the war shows how significant the impact of these atomic bombs was. So unrelating was the Japanese effort to keep fighting despite the fact that they were losing, soldiers were prepared to die in Kamakzie attacks, even if they were not very successful. It was only when the Empire was faced with a weapon that could wipe out an entire nation that they agreed to unconditionally surrender (9).

Was the detonation justified?

This is a highly controversial topic, and one that is hotly contested. Historians including Antony Beaver argue that they were justified, explaining that not in the past 2,600 years had there ever been a historical record of a Japanese surrender, and that reports from Japanese documents indicate that their army was prepared to accepted up to 28 million deaths, which is 140 times more than the casualties caused by the atomic explosions (10). Richard Frank explains how civilians had been forced to fight with bamboo sticks, such was the unwillingness to surrender, and only the destructive power of a nuclear bomb could have brought about this capitulation (11). Historian Richard Overy disagrees, arguing that not only would Japan have surrendered anyway when faced with the total invasion by the Soviet Union just days before the second bomb exploded, but the fact that the Americas actually used the bomb, demonstrated to the world that nuclear warfare was acceptable and signalled the start of the cold war and the Nuclear arms race (12).

It is true that the physics of fission and Einstein’s equations were used in the killing of civilians. Without scientists work on the Manhattan project, there would have been no destruction of Hiroshima. But sciences ultimate goal in this project was to liberate the world of fascist dictators. Physics was indeed weaponised, not for the malice of harming civilians (this was a secondary factor), the primary factor being to defend the allied powers and bring peace to Earth.

The state of ruin Hiroshima was left in after the dropping of 'Little Boy'

The Hydrogen bomb

The first Hydrogen bomb was developed and tested on the 1st November, 1952 and was developed by scientists including Edward Teller and Stanislaw M. Ulam. There are fundamental differences between hydrogen bombs and atomic bombs, the main one being is that the hydrogen bomb uses both fission and fusion process to initiate and explosion, but the latter only includes fission. A hydrogen bomb consists of two main components, a nuclear fission primary stage that is fuelled with either U-235 or P-239, and a separate nuclear fusion stage which contains heavy hydrogen isotopes such as H-2 and H-3 (deuterium and tritium)(13). 

The explosion begins with the detonation of the fission fuel in the primary stage.as shown in 1). The fission process releases energy as explained prior, as mass is converted into binding energy of the fissile products. This causes the temperature in the compartment to reach around 100 million kelvins (20,000 times hotter than the surface of the sun) and this emits X-Rays through thermal radiation (the same waves used in an X-ray machine just with far more energy). The X-Rays then travel to the secondary fusion compartment as in 2), and implodes the plutonium spark plug, which in turn compress the fuel using a pusher. The density of this Plutonium fuel rises and hence the mass becomes supercritical (like in the Plutonium-fission bomb) and begins a nuclear fission chain reaction. This is because the polystyrene foam becomes a plasma at this high temperature, which in turn buts more pressure and squeezes the plutonium as in 4). The energy created in this explosion heats the second compartment to around 300 million kelvin, which is hot enough to ignite fusion reactions between the hydrogen isotopes. The hydrogen isotopes fuse together to form helium, and this reaction releases and immense amount of energy, as explained earlier. The two assemblies are separated, to ensure that the fission explosion does not dissemble the secondary compartment. Since X-Rays travel at the speed of light, they travel much faster than the neutrons emitted from fission, and hence reach the fusion fuel first. Consequently, in order for the fusion reaction to take place before the fission reaction destroys the entire compartment, the time from ignition to explosion is around 1 microsecond (which is around a thousand times shorter than a lightning strike) (14).

The journey from ignition to explosion in a hydrogen bomb

The fission weapons described prior have a theoretical limit to their yield, and the largest weapon ever developed only had a yield of 500 kilotons. Fusion weapons have no such upper limit, and the largest one ever tested, called the Tsar bomb, had a yield of 50 megatons, which is equivalent to 45,000,000 kg of TNT.  Its mushroom cloud soared up to 67 km above the ground (7 times higher than Mount Everest) (15). The sound released from this bomb was around 250 dB, which is over 100 Billion times louder than the noise of a jet engine (16). If the searing heat or powerful shockwave did not kill you, then the sheer intensity of the sound would. However, tactical and battlefield nuclear weapons have yields that are often less than a kiloton, since too big a blast will annihilate both friendly and enemy troops.

The true danger of hydrogen bombs can be seen in how so few countries possess them. Only 6 countries: The United States, France, Russia, the United Kingdom, India, and China have conducted thermonuclear weapons tests. the fact that five out of 6 of these countries have Veto powers on the UN security councils, indicate that only the major powers in the world occupy these weapons, despite the fact they were first designed over 60 years ago. The Iran Nuclear treaty illustrates the concern major powers treat a new country that attempts to enrich uranium in order to build a nuclear weapon (17). The deal orders that Iran reduce its enriched Uranium stockpile by 98% or face heavy sanctions on military equipment and financial services. In fact, many of the scientific details behind fusion weapons are classified information, such is the precarious nature of this knowledge. In the US, knowledge about fusion weapons is labeled as “restricted data”  even if this knowledge was discovered independently. Therefore, it is technically illegal for you to find new knowledge about fusion weapons, and this legal doctrine is known as the “born secret” (18)

The peculiar mushroom cloud shape of a deadly thermonuclear explosion is independent of the contents or type of explosion that occurs. It actually depends on how powerful the detonation was. A mushroom cloud only forms when the explosion is so hot, that it creates a very hot bubble of gas. The hydrogen bomb creates a temperature hot enough that it will release a barrage of X-Rays which ionise the surrounding air, and this hot bubble is known as a fireball.  This air becomes buoyant and rises quickly and expands. If the fireball rises high enough to reach the boundary between the troposphere and the stratosphere (located around 50 km above ground), then the cloud is formed. This is because there is a strong temperature gradient between the two atmospheres, preventing the layers from mixing. The fireball no longer has enough energy to break through this boundary and can no longer rise any higher. This is why it flattens out and expands to the side into an exaggerated mushroom cap. This effect is also observed in large summer thunderclouds when they rise up to the tropopause, producing this anvil like shape (19).

The Mushroom Cloud effect on a hydrogen bomb explosion
Mushroom effect on a cumulonimbus cloud

Nuclear power, benefit or hinderance?

The accelerated understanding of fission (through programmes like the Manhatten project) and its implementation in bombs that release kilotons of TNT, provided evidence to scientists and governments alike, that fission could be used to produce energy. Nuclear power produced over 2,586 TWh of electricity in 2019, equal to around 10% of global electricity generation. Furthermore, there are 442 civilian reactors in the world. This source of energy benefits us. Not only does Nuclear power have the lowest levels of fatalities compared to other energy sources such as coal, but it is also relativity clean, as it does not emit harmful greenhouse gases that contribute towards climate change. The only problem with this energy source (not including the reactor meltdowns that have occurred in Chernobyl and Fukashima) is that, at the current rate of consumption, we only have 80 years left before our nuclear fuel runs out (20).

The astute readers who have been paying attention might question why fission is used in nuclear fuel, and not fusion, since as we discussed earlier, fusion reactions which hydrogen produce more energy per unit mass. This is for two reasons, firstly, fusion reactions aren’t self-sustaining, and don’t produce chain reactions, so it is difficult to leave the reaction to run and produce energy. Secondly, the temperature for nuclear fusion to occur is so high, that the pressure needed to achieve these temperatures using current techniques would use more energy than the fusion reactions would ever release. However, the future of nuclear fuel rests in the hands of fusion. Deuterium, a source of fuel needed for fusion, occurs naturally in seawater, and whilst Tritium is far rarer,  it can be bred in a nuclear reactor using Lithium, which is far more abundant. The abundance of fusion fuel, coupled with the larger amounts of energy released (the power output is predicted to be 4 times higher than for a fission reactor) gives humanity the prospect of an inexhaustible source of energy for future generations. However, this is juxtaposed with the currently insurmountable engineering challenges and so introduces a dilemma as to whether countries should heavily invest in the technology. In France, Magnetic Confinement Fusion (MCF); where strong magnetic fields allow Deuterium-Tritium plasma to be at high enough densities for fusion to occur, is being studied closely. The magnetic force allows the fuel to not be in contact with the reactor walls, meaning far less heat is dissipated. These reactors, called Tokomaks, are projected to be commissioned for use by 2027. However, this reactor will be a development project, and commercial fusion power stations are not expected to be in use until 2050 as suggested by ITER (international nuclear fusion research and engineering megaproject) (21).

The future of fusion power presents exciting prospects but difficult engineering obstacles

Without World War Two, it is hard to see how the Atomic bomb could have been developed anywhere to 1945. there was no need for such an upgrade, and the science was not well understood. The war utilised physics to harness the energy released from fission  and turned is so powerful it was vowed never to be used again. This is not the direct fault of physics, there is a plethora of physics that can be used for damage, however, only circumstances, like war, provide suitable conditions for this physics to be utilised. 

However, I hope you as a reader have seen that the science of fission can also benefit humanity. Einsteins equations show that this release in energy can be used in power stations, and the sheer notion of fusion power stations should make you feel optimistic. This energy would be near inexhaustible, and will help in the battle against climate change. The science behind fusion power stations is too hard you say? Well, consider that a nuclear bomb, was theorised, designed, developed, tested and dropped within a space of 4 years. Anything is possible.  

References

  1. https://www.atomicheritage.org/history/little-boy-and-fat-man
  2. A. Einstein (translated by W. Perrett and G.B. Jeffery), Does the inertia of a body depend upon its energy contents. (1905)
  3. Joel Rhodes, Kord Smith, Zhiwen Xi; Energy release per fission model. Studsvik Scandpower Inc., Idaho Falls, USA (pp. 3)
  4. https://www.measuringworth.com/datasets/usgdp/
  5. Hewlett, Richard G.; Anderson, Oscar E. (1962). The New World, 1939–1946 (PDF). University Park: Pennsylvania State University Press.
  6. Jones, Vincent (1985). Manhattan: The Army and the Atomic Bomb (PDF)
  7. http://blog.nuclearsecrecy.com/2012/04/16/oak-ridge-confidential-or-baseball-for-bombs/
  8. https://www.realclearscience.com/blog/2019/09/12/the_fear_that_a_nuclear_bomb_could_ignite_the_atmosphere.html#:~:text=In%201942%2C%20Hungarian%2DAmerican%20physicist,the%20atmosphere%20and%20the%20oceans.
  9. https://www.carnegiecouncil.org/education/008/expertclips/010
  10. Should America have dropped bombs on Hiroshima and Nagasaki. BBC History magazine (2015)
  11. Richard B.Frank; Downfall: The End of the Imperial Japanese Empire, New York: Random House, 1999, 484 pp.,
  12. International Review of the Red Cross; The evolution of warfare: interview with Richard Overy (2015)(97,900)
  13. Herman Wolk; Making of the H bomb
  14. https://www.britannica.com/technology/thermonuclear-bomb
  15. http://www.johnstonsarchive.net/nuclear/multimeg.html#S2
  16. https://www.customaudiodirect.co.uk/understanding-decibels#:~:text=Normal%20conversation%20%2D%2060%20dB,a%20jet%20engine%20%2D%20120%20dB
  17. https://www.cfr.org/backgrounder/what-iran-nuclear-deal
  18. Howard Morland; Born Secret, Cardozo Law Review, VOL 26, MARCH 2005
  19. https://www.scientificamerican.com/article/what-are-the-processes-th/
  20. https://www.iea.org/news/steep-decline-in-nuclear-power-would-threaten-energy-security-and-climate-goals
  21. https://web.archive.org/web/20061107220145/http://www.iter.org/Future-beyond.htm
All pictures have there relevant links attached to them (the balance diagrams were self made)

Struggling? Click the highlighted words for more info, or check the                             appendix out for more information