Physics behind the Horror of Hiroshima

E=mc² Unleashed!

In 1938, four German scientists were involved in a discovery that would soon alter the course of history. They split the uranium atom and ushered in the Atomic Age, highlighted by the horror of Hiroshima on 6 Aug 1945.

[This article is in the nature of an appendix to my Japan travelogue Part B (see here), where I wrote about my experience in Hiroshima, its iconic Atomic Bomb site and the adjacent Peace Park, in June 2018. I had made a detailed reference to the enormous destruction caused by the first ever nuclear attack on a human populace. A reader had suggested that some explanation of the physics behind the destructive power of the weapon was also desirable, especially considering that I have a master’s degree in Nuclear Physics.  I thought it would be appropriate to write a separate article on the topic in non-technical language, and here it is!]

This is ‘Little Boy’, the A-bomb dropped on Hiroshima, being loaded
into the weapons bay of the B-29 bomber Enola Gay

Foreword

We all have an intuitive understanding of the terms matter and energy.  For example, wood is matter, and fire, which we see when wood is burnt, is a manifestation of energy; when we stand in the hot Sun, the Sun and ourselves both are matter, and the sensation of heat in our body is the result of the energy generated at the Sun and getting absorbed in our body.  However, most people find it hard to understand how it is possible to convert small amounts of matter totally into enormous amounts of energy, as with the nuclear weapons dropped on Hiroshima and Nagasaki towards the end of the Second World War. Answering this question involves a deep study of the concepts of matter and energy, the composition of matter in terms of some fundamental building blocks, and how it is possible to break up the subatomic nuclei and release the energy stored in them at the time of their formation.

In this article, I will first present an overview of the structure of matter and its relation to energy, and then describe in brief the technology that came to be created and used to transform this knowledge eventually into bombs that were employed in the Second World War.

For reasons of cohesion and continuity, I have found it necessary to introduce many technical terms and expressions without elaborating on them adequately, so as to avoid a lengthy article.  Readers may find the weblinks provided in such cases helpful for a deeper understanding.

It is not my purpose to discuss the politics behind the creation of nuclear weapons and their eventual use, much less the nuclear politics in the world since 1945.  Rather, I shall restrict myself to just the physics of nuclear fission, and touch upon some technical aspects of weaponization.

The horrors brought about by the dropping of the atomic bomb, first on Hiroshima (a city I visited) and then on Nagasaki, impelled me to present this article to my readers as a non-technical appendix to my travelogue on Hiroshima.

Composition of Matter

The idea that all matter is made up of some ‘fundamental’ building blocks dates back to ancient history when some thinkers regarded these to be familiar substances like air, water, fire, earth, etc.  By the early twentieth-century the picture had changed dramatically, influenced by the atomic theory of matter of John Dalton (1766-1844). The building blocks had expanded to 92 stable elements, ranging from hydrogen to uranium, and classifiable into recognizable groups within the periodic table of elements conceived by Dmitri Mendeleev (1834-1907) (see chart below). 

The Nuclear Atom 

The smallest particle (atom) of each element consists of specific numbers of more fundamental ‘particles’ called protons, neutrons, and electrons, with the protons and neutrons (collectively called nucleons) bound tightly together into a nucleus at the center of the atom, and a cloud of virtually massless electrons spread around the nucleus, very far away, but still within the atom.  This means that the atom is an enormous void, with an incredibly small fraction of its volume, and an enormously large fraction of its mass, accounted for by the constituent particles. Pictorial representations of the structure of an atom are as far removed from reality as those of the solar system, with its Sun and the planets!

Practically all the mass of the atom could be attributed to the nucleus.  The proton was found to be about two thousand times the mass of the electron, with the (free) neutron being very slightly more massive than the proton.

Electric charge was recognized as an important property of the electrons and protons, each electron having the same amount of charge as the proton, but of the opposite sign (negative).  The element as a whole is normally electrically neutral since the number of electrons in it is the same as the number of protons, the chemical property of the element depending crucially on this number and the distribution of electrons in the electron cloud surrounding the nucleus.

Work and Energy

In physics, the terms work and energy have specific connotations, being measurable entities, unlike in common parlance.  Work is said to be done when a force applied on a body displaces it from its initial position and is measured by the product of the force applied and the component of the displacement in the direction of the applied force. Energy is the capacity to do such work and manifests itself in various forms – mechanical (kinetic and potential), thermal (heat), chemical, electrical, electromagnetic (which includes visible and invisible light, x-rays, gamma rays, radio waves and microwaves), nuclear, gravitational – and can be generally transformed from one form to another.  During these transformations, the total energy of the system doesn’t change, only the form.  This is the principle of conservation of energy. Some of these transformation processes are readily recognizable, such as heat into light, electrical into heat and light, mechanical into electrical, etc.  However, transformations involving nuclear energy are more subtle and rarely noticed in everyday life.

Matter and Energy

Here is something the lay reader may find puzzling and difficult to comprehend. Matter and energy are not only mutually interchangeable, they are fundamentally one and the same as shown by Einstein’s seminal Special Theory of Relativity.  Mass is an intrinsic property of matter.  Mass (m) and energy (E) are quantitatively connected by the relation E=mc², where c is the speed of light (c= 3x10⁸ m/sec). Matter (mass) and energy are like the two faces of the same coin. Measured in energy units, as is generally the practice in subatomic physics, matter is the same as the rest energy of a system. At the subatomic level, matter can be looked upon as a strongly compacted form of energy.

Particle Attributes

At whatever level, particles have several key attributes like mass, charge, and spin.  The masses of particles are generally expressed in equivalent energy units since mass and energy are basically the same.  The unit employed is the electron volt (eV) which is the energy gained by an electron in crossing an electrical potential difference of one volt. Since it is a very small unit, energies are expressed in units of keV, MeV, GeV, and TeV. Accordingly, the mass of an electron is 0.511 MeV and that of a proton 938.27 MeV. The mass of a free neutron is 939.57 MeV.   The charge of a particle may be positive (+), negative (-) or zero.  Spin is a purely quantum mechanical property, loosely analogous to the rotation of a rigid body.  For reasons yet to be fully understood, nature makes a major distinction between particles of half-integral spin, called fermions, and particles of integral spin (including zero), called bosons.

Isotopes

Most elements consist of isotopes, which belong to the same family and name, with the same number of protons (Z), but with differing number of neutrons (N), leading to differing masses (called atomic mass, A) as a whole, and differing abundances as well. An isotope is often designated by the symbol _zX^A, where Z is the number of protons, also called charge number and A the atomic number. The isotopes of an element are chemically indistinguishable, but their physical differences, arising out of differing atomic masses, can be easily studied.

The following table gives some data in respect of a few well-known elements and their stable isotopes:

 

Name	Symbol	Atomic Number, A	Number of protons, Z	Number of Neutrons, N
Hydrogen Deuterium	1H1 * 1H2	1 2	1 1	0 1
Helium	2He3 2He4 *	3 4	2 2	1 2
Carbon	6C12	12	6	6
Oxygen	8O16 * 8O17 8O18	16 17 18	8 8 8	8 9 10
Aluminum	13Al27	27	13	14
Chlorine	17Cl35 * 17Cl37	35 37	17 17	18 20
Iron	26Fe54 26Fe56 * 26Fe57 26Fe58	54 56 57 58	26 26 26 26	28 30 31 32
Silver	47Ag107 * 47Ag109	107 109	47 47	60 62
Gold	79Au197 #	197	79	118
Lead	82Pb204 82Pb206 82Pb207 82Pb208 *	204 206 207 208	82 82 82 82	122 124 125 126
Uranium	92U235 ^ 92U238 *	235 238	92 92	143 146

                                  * Most abundant isotope of the element

                                  # Heaviest monoisotopic element

                                  ^ Fissionable isotope, present in only 0.7% of natural uranium

Radioactive Decay

An unstable nucleus, commonly described as radioactive, loses its excess energy by radiating it, usually in the form of alpha particles (which are highly stable helium nuclei made of two protons and two neutrons), beta particles (which are just electrons) or gamma rays (which are highly energetic electromagnetic radiation).  In the process, called radioactive decay, both mass/energy and electric charge are conserved, i.e., the total mass/energy and net charge remain unchanged.

The following examples illustrate each of these three processes:

₉₄Pu²³⁹ ---> ₉₂U²³⁵ + ₂He⁴                                                [α-decay]

₆C¹⁴ ---> ₇N¹⁴ + _-1e⁰ (+ antineutrino)                                [β-decay]

₆C¹⁰ ---> ₅B¹⁰ + ₊₁e⁰ (+ neutrino)                                      [β-decay]

₂₇Co⁶⁰ ---> ₂₈Ni⁶⁰ + _-1e⁰ + γ (gamma photon)                  [γ-decay]

Observe that the net charge (subscripted) and net mass/energy (superscripted) are the same (i.e., conserved) before and after these and all other such transformations.

Induced Radioactivity

Often, stable nuclei can be made radioactive by bombarding them with ionizing radiation such as gamma rays or neutrons from a naturally radioactive material or from accelerated charged particles such as electrons, protons, and alpha particles using appropriate particle accelerators.  Here is an example:

₅B¹⁰+₂He⁴ ---> ₇N¹³ + ₀n¹            [Bombardment by α-particle]

₇N¹³ ---> ₆C¹³ + ₊₁e⁰ (+ neutrino) [Decay of artificially radioactive element]

Over 3,000 radioisotopes (most of them induced) are known. Only a small fraction of these can be found in nature.  In contrast, the number of stable isotopes is 254.

It is interesting to note that the renowned Marie Curie (1867-1934) contributed to the discovery of natural radioactivity at the turn of the last century, and her daughter, Irene Curie (1897-1956), had a hand in the discovery of induced radioactive in 1934, each winning the coveted Nobel Prize.

Marie Curie (right) with daughter Irene Curie

Decay Half-life

The time taken for half of the radioactive nuclei of a particular isotope to decay into another species is called its half-life. Half-lives of radioactive materials vary over a very wide range, from nanoseconds to billions of years (for virtually stable elements). After about seven half-lives, less than one percent of the original material will be left over.  Here are a few examples:

₆C¹⁴ ---> ₇N¹⁴ + _-1e⁰ (+ antineutrino)        has a half-life of 5700 years

₉₂U²³⁵ ---> ₉₀Th²³¹ + ₂He⁴ (α-particle)     has a half-life of 704 million years

₂₇Co⁶⁰ ---> ₂₈Ni⁶⁰ + _-1e⁰ + γ (photon)       has a half-life of 5.27 years

₅₃I¹³¹ ---> ₅₄Xe¹³¹ + _-1e⁰                                 has a half-life of 8 days

Nuclear Binding Energy

Nuclear Binding Energy is the minimum amount of energy, generally expressed in units of MeV or GeV, required to split an atomic nucleus into its constituent nucleons (protons and neutrons).   In this context, a related useful quantity is the mass defect, which is the difference between the calculated mass and the actual mass of the nucleus. The binding energy accounts for the difference in mass and is given by E= Δmc², where Δm is the mass defect and c, the speed of light (c = 3x10⁸ m/sec), from Einstein’s Special Theory of Relativity.

A classic example is the alpha particle (which is the same as the stable helium nucleus): Its mass is 4.001506 u (u being the atomic mass unit).  The mass of a neutron and proton are respectively, 1.008665 u and 1.007276 u. The mass defect is therefore 2x (1.008665+1.007276) u – 4.001506 u = 0.030376 u. Since 1u = 931.5 MeV, the mass defect translates to a binding energy of 0.030376x931.5 MeV = 28.295 MeV, which means an exceptionally high binding energy and hence correspondingly high stability of the nucleus. 

Now, let us see how the binding energy varies across the nuclear species.  In the following graph, the mean binding energy per nucleon (which, for the alpha particle, works out to be 28.295/4 MeV = 7.073 MeV) is plotted against the atomic mass number. 

Observe that:

• The binding energy per nucleon (BE) reaches a peak of 8.8 MeV in the neighborhood of mass number 56, corresponding to Iron.
• In the realm of low mass, the BE decreases rapidly with mass number.
• In the realm of high mass, the BE decreases slightly as the mass number increases.
• Fusion of light nuclei into heavier ones below iron in the periodic table results in tighter bound nuclei, i.e., a net increase in binding energy.
• Break-up of nuclei into lighter ones above iron in the periodic table results in less tightly bound nuclei, i.e., a net decrease in binding energy.

Nuclear Fission

In 1938, German chemists Otto Hahn (1879-1968) and Fritz Strassman (1902-1980) discovered a strange result when Uranium was bombarded by neutrons. The main products of the induced radioactivity were nearly half way down in the periodic table (mainly barium and krypton isotopes) instead of being close to it as was known till then. This puzzling phenomenon was explained by physicist Lise Meitner (1878-1968), and her nephew Otto Frisch (1904-1979), as due to the break up (fission) of the target nucleus into much lighter nuclei, with a substantial amount of the nuclear binding energy of uranium being liberated.  Equally puzzling was the denial of the 1944 Nobel Prize to Lise Meitner, while recognizing the contribution of Otto Hahn to this history making discovery, of nuclear fission.

Lise Meitner & Otto Hahn

The process of nuclear fission is represented below diagrammatically: 

Nuclear fission chain reaction

A typical and highly probable nuclear fission reaction, when a uranium 235 nucleus absorbs a neutron and the resulting compound nucleus breaks up immediately into fragments, is shown below:

₉₂U²³⁵ + ₀n¹ ---> ₅₆Ba¹³⁹ + ₃₆Kr⁹⁵ + 2₀n¹ + 200 MeV (approx) energy   

What is most significant is that more neutrons are produced than are absorbed by the target nucleus.  This means, a rapidly progressing nuclear chain reaction of the type depicted below is possible:

If each neutron releases two more neutrons, then the number of fissions doubles each generation.  In that case, in 10 generations there are 1,024 fissions and it takes only about 80 generations to produce a mole (6 × 10 ²³) of fission products, accompanied by truly gargantuan amounts of energy.  All this happens in a matter of microseconds in an uncontrolled device like an A-bomb!

After Uranium 235, it was soon discovered that Plutonium 239 was similarly fissionable and became quickly recognized as another source of fuel, for both nuclear reactors and weapons.  Plutonium 239, is a man-made, transuranic element, produced when the U 238 isotope in natural uranium-fed nuclear reactors absorbs a fast neutron and decays into this element according to the following successive beta decays:

₉₂U²³⁸ + ₀n¹ --- ₉₂U²³⁹ --- ₉₃Np²³⁹ + _-1e⁰ + antineutrino

₉₃Np²³⁹ --- ₉₄Pu²³⁹ + _-1e⁰ + antineutrino

When bombarded by neutrons, Plutonium 239 splits into smaller fragments as does Uranium 235, and produces two or more neutrons, and a little over 200 MeV of energy as well.

Self-sustaining Chain Reaction

A nuclear fission chain reaction is said to be self-sustaining if the number of neutrons released in a given time equals or exceeds the number of neutrons lost by absorption in non-fissionable material or by escape from the system in the same time. The attainment of this was crucial to any scheme of releasing fission energy on a large enough scale to be of any practical use.  The Hungarian physicist Leo Szilard (1898-1964) developed this idea, discussed the implication of this for the development of a nuclear weapon (the A-bomb) with the legendary Albert Einstein, and persuaded the latter to write a historic letter to then US President Franklin Roosevelt, and paved way for the top-secret wartime Manhattan Project whose goal was to actually develop such a weapon.  American physicist Robert Oppenheimer (1904-1967) was the overall leader of the project. 

Leo Szilard (right) with Albert Einstein

It was left to the genius of the great Italian physicist Enrico Fermi (1901-1954) to achieve the world’s first self-sustaining nuclear chain reaction, and release of a tiny but measurable amount of nuclear energy, with a ‘pile’ of Uranium 235 at one corner of an unused football stadium of the University of Chicago on 2 December 1942.  This was the precursor to both the A-bomb with its uncontrolled, and the nuclear reactor with its controlled, release of large amounts of nuclear energy, serving both destructive and constructive purposes. The reactor consisted of natural uranium and uranium oxide lumps of ‘fuel’ spaced in a cubic lattice embedded in graphite, which was also meant to slow the neutrons to thermal energies needed for maximizing the fission probability.  Here is a picture of the historic ‘Chicago pile’, no longer to be found in its original location as I sadly discovered during my visit there sometime in 1967:

Enrico Fermi

The Chicago Pile

Instead of the pile itself, I found the following plaque to commemorate the historic event. The emphasis in it is on the word ‘controlled’ for that is exactly what it was meant to do, and it served as the forerunner of much larger and more complex nuclear reactors, marking the advent of peaceful uses of nuclear energy.

[Postscript: I distinctly remember to have had my picture taken against the background of such a plaque, but the picture is sadly untraceable. Unfortunately, that was very much the era of cumbersome ‘chemical’ photography!]

Critical Mass

The critical mass of a fissionable material is the minimum amount of the material that will support a self-sustaining chain reaction. At any instant in a critical mass assembly, the number of neutrons freshly generated by fission is equal to the number of neutrons lost from the system at its surfaces. The neutron multiplication factor, which is defined as the ratio of the neutrons generated in any particular generation to the number of neutrons in the previous generation, is exactly 1 for the critical mass of any material. If the factor is less than one, the mass is said to be subcritical, and there is no danger of a spontaneous explosion.  But, if the factor is greater than one, the mass is said to be supercritical, and spontaneous explosion is a possibility, unless protected by suitable control systems, like a cadmium rod inserted into the mass to absorb excess neutrons and keep the multiplication factor under control.

The A-Bomb

Once the self-sustaining nuclear chain reaction and controlled release of nuclear energy was achieved, the attention of the Manhattan project scientists turned to the goal of weaponizing the system, which was the basic objective of the project, apparently forced upon science by the ongoing World War II.

Unlike a nuclear reactor, a nuclear weapon of whatever design requires to be small and light enough to be carried by a high-flying bomber aircraft of the times and capable of handling much like a conventional weapon.  Also, a significant fraction of the fuel should be consumed before the weapon destroys itself.

In a sample of naturally occurring uranium, only the U 235 isotope is fissionable by neutron capture, and it accounts for only 0.7% of the uranium as such (most of it being the slightly heavier U 238 isotope).  Therefore, the explosive material of a bomb has to be pure U 235 or very highly enriched uranium in which the U 235 content has to be higher than 90% at least to meet operational requirements. This forced the scientists to design, build and operationalize massive isotope separation/enrichment facilities, both chemical and physical, literally on a war footing, with the immediate objective of securing a sufficient quantity of the fissionable material, assembling a workable bomb, and testing it, even as the fissionable isotope stockpile continued to build up.

After the early nuclear reactors had run long enough, plutonium 239, extracted from their spent uranium fuel, became a second source of abundant nuclear energy.

The strategy that emerged for detonating the A-bomb was to bring about the rapid formation of a supercritical mass of the material from two or more smaller subcritical masses or from the rapid implosion of a spherical mass, which would also bring about the same effect because of the increase of neutron density in the collapsing core. The two­ strategies are depicted in the following diagram: 

The Trinity Test    

Trinity was the code name of the first detonation of a nuclear weapon on 16 July 1945, as part of the Manhattan Project. The test was conducted in a desert about 56 km southeast of Socorro, New Mexico, on what was then the Alamogordo Bombing and Gunnery Range.  A base camp was constructed, and there were 425 people present at the time of the test. The test was of an implosion-type plutonium device, nicknamed ‘The Gadget’, of the same design as the 'Fat Man' bomb later detonated over Nagasaki, Japan, on 9 August 1945.  The device was placed on top of a 30m steel tower pictured below with the device itself shown in the inset. Also shown is the ‘mushroom’ cloud formed over the test site, engulfing and swallowing up everything in and around, immediately after the blast.

Robert Oppenheimer, who was also a Sanskrit scholar (having acquired a knowledge of the language in the 1930s when he taught at Berkeley), later recalled: “We knew the world would not be the same. A few people laughed; a few people cried. Most people were silent. I remembered the line from the Hindu scripture, the Bhagavad Gita; Vishnu is trying to persuade the prince (Arjun) that he should do his duty and, to impress him, takes on his multi-armed form and says, 'Now I am become Death, the destroyer of worlds.' I suppose we all thought that, one way or another.”   

 J Robert Oppenheimer

The Yield

The explosive (energy) yield of a nuclear weapon is the amount of energy released such as blast, thermal, and nuclear radiation, when that particular nuclear weapon is detonated. It is usually expressed as a TNT equivalent (the standardized equivalent mass of the conventional explosive trinitrotoluene which, if detonated, would produce the same energy discharge). Incidentally, an explosive yield of one terajoule is equal to 0.24 kilotonnes (kT) of TNT.  On this scale, the Trinity test yield was estimated to be 21 kT.    This too was the scale of the horror soon to unfold on Hiroshima!  The mass of Plutonium making up the weapon was only about 6 kg.

Bombing of Hiroshima

On that fateful morning of 6 Aug 1945, the ‘Little Boy’, dropped on Hiroshima, was a Uranium 235 device with a yield of about 15 kT.  It was carried aloft the bomber Enola Gay, piloted by Paul Tibbets, who had the dubious distinction of unleashing the horror of Hiroshima.

Enola Gay with pilot Paul Tibbets at center

The Aftermath

To drive home the magnitude of the horror of Hiroshima, here are a few of the terrifying facts (also listed in my Hiroshima travelogue earlier):

·        “Nothing remained except a few buildings of reinforced concrete… For acres and acres, the city was like a desert except for scattered piles of brick and roof tile.”

·        Those who were close to the epicentre of the explosion were simply vaporized by the intensity of the heat. The others were luckier in simply being charred to death.

·        Many objects and people in the path of the intense light and heat spreading out from the explosion absorbed the energy and only their ‘nuclear shadows’ on walls and pavements survived. The objects and people had disappeared into oblivion.

·        “Doctors realized in retrospect that even though most of the dead had also suffered from burns and blast effects, they had absorbed enough radiation to kill them. The rays simply destroyed body cells - caused their nuclei to degenerate and broke their walls.”

·        Some 70,000 - 80,000 people, around 30 percent of the population of Hiroshima at the time, were killed by the blast and resultant firestorm, and another 70,000 were injured.

·        69 percent of Hiroshima's buildings were destroyed and another 6 to 7 percent damaged.

·        Over 90 percent of the doctors and 93 percent of the nurses in Hiroshima were killed or injured - most had been in the downtown area which received the greatest damage. The hospitals were destroyed or heavily damaged.

·        The plight of most survivors was worse than death. They suffered a slow, agonizing death caused mainly by the effects of gamma rays and neutrons, the main products of nuclear fission of the bomb material. 

 Source: Hiroshima Peace Memorial Museum

Located close to the hypocenter, the building in the picture above received the blast from almost directly above, which allowed some of the center walls to escape collapse. The steel skeleton of the dome became a symbolic landmark for the horror of Hiroshima. And this is where I spent some of the saddest moments of my life, contemplating the horror, and shedding tears for the plight of innocent people at the hands of the high and the mighty.

[PS: I am highly indebted to distinguished academician Dr Anil Kumar Belvadi, for his incisive comments, feedback and suggestions on this and the whole of my previous Japan travelogues.]