Monday, January 26, 2015

Chemical Explosions Versus Nuclear Explosions: Where The Energy Comes From

The previous article focused on chemical explosives such as nitroglycerin, TNT, picric acid and cyclonites. This article focuses on what distinguishes a chemical bomb from a nuclear bomb by taking a close look at what is going on at the atomic level.

Nuclear Devices

A nuclear explosion is a very high-speed nuclear reaction. These explosions release energy from bonds that hold nuclei together inside atoms. The nuclear process in a nuclear device or bomb may be one of fission (splitting atomic nuclei) or a multistage combination of fusion (combining atomic nuclei) and fission, where fission initiates a fusion reaction (there are no pure fusion bombs in existence). We will explore in detail how fission and fusion weapons work in the next article. A chemical explosion, in contrast, is a chemical reaction in which the nucleus stays intact while electron bonds between atoms in the explosive compound are broken and new ones are created.

Explosive Yields of Nuclear Devices Compared to Chemical Explosives

A nuclear weapon yields far more explosive energy than any chemical weapon. Still, it is conventional to describe the amount of energy released by a nuclear detonation as TNT equivalent. For example, the Fat Man nuclear bomb that dropped on Nagasaki released the equivalent of about 22 kilotonnes (kt) of TNT. Fat Man, an implosion-style plutonium bomb, was not very powerful compared to many other nuclear devices, It was a thousand times less powerful than later large nuclear fission bombs that were developed, and about ten thousand times less powerful than the first hydrogen bombs.

Yet, as we touched on in the previous article, this nuclear explosion was ten times more powerful than the Halifax chemical explosion, one of the largest explosions in history. Hydrogen bombs (H-bombs or thermonuclear bombs) are the most powerful bombs of all. The first H-bomb tested was Ivy Mike. It was detonated in 1952 by the U.S in an atoll in the Pacific Ocean. This bomb was equivalent to 10.4 Mt (mega or million tonnes). If we compare this to the 22 kt yield of Fat Man, it is about 500 times more powerful. Ivy Mike's detonation is shown below right.

The Official CTBTO Photostream;Wikipedia
The Halifax explosion was devastating but it was not the largest chemical explosion on record. That distinction goes to the accidental N1 rocket launch explosion in 1969. This heavy-lift Soviet rocket exploded on the launch pad after a loose bolt was ingested into a fuel pump. Designed for very large payloads, it contained 680 tonnes of kerosene and 1780 tonnes of liquid oxygen. It is difficult to estimate how much of this explosion was detonation and how much of it was deflagration, as the two fuels were unmixed when it went off, but its energy was roughly equivalent to 7 kt of TNT (the Halifax explosion was equivalent to 2.9 kt). The photo below left gives you an idea of what this huge type of rocket looked like. The U.S. Saturn V, which it was built to compete with, is on the left for comparison.


The yields of various nuclear devices range enormously, from 0.01 kt (10 tonnes TNT equivalent) for low-yield tactical nuclear weapons to an utterly devastating 50 Mt. This was the yield of Tsar Bomba, the most powerful H-bomb (and therefore the most powerful artificial explosion) ever detonated. Russian-made, it was detonated in the Russian archipelago, Novaya Zemlya. A participant in the experiment felt the heat from it 270 km away. The shockwave broke windowpanes as far away as 900 km. The 8-minute video below, from the History Channel, discusses Tsar Bomba and provides a chilling account of what happens when a hydrogen bomb like this one detonates.

To get an idea of the variability in nuclear weapon yields, the graph below compares the yields of various nuclear weapons developed by the U.S. (Russian Tsar Bomba would be off this scale). It plots yield in kilotonnes (kt) against weapon weight in kilograms (kg). Note that the kt scale is a logrhythmic scale. (Little Boy, near fat Man below, is the nuclear bomb dropped on Hiroshima three days before Fat Man dropped on Nagasaki. It was a gun-type uranium fission bomb.)

A Brief Look at Nuclear Weapons and Warfare

We often associate nuclear explosions with terrifying mushroom clouds but actually both chemical and nuclear reactions can produce these kinds of clouds. Even naturally occurring volcanic eruptions can produce them. These clouds can form at any altitude from the sudden release and expansion of gases that are less dense than the air around them. The cloud is buoyant so it rises rapidly. Instability inside the cloud creates turbulent vortices that curl downward around the edges forming a vortex ring that draws up a central column or stem.

Wikipedia Commons
The central stem contains smoke, debris, which can include tonnes of dirt, and condensed water vapour. When the cloud reaches equal pressure with thinner air at higher altitude, it begins to disperse and debris drawn up begins to drift back down as fallout. If it is a nuclear bomb, this fallout will contain radioactive dust and debris: atoms in the dirt and debris are bombarded with fast moving neutrons emitted during the reaction. These atoms in turn, absorbing extra neutrons, also become unstable and radioactive (I will explain this process further on in this article).

Below, a horrific mushroom cloud forms after Fat Man detonated on Nagasaki, Japan in 1945.

Unique to nuclear explosions, and part of what makes them so deadly, is that in addition to the impact, the intense heat and the shock wave of the explosion, the reaction also scatters highly radioactive reaction products and fallout into the air, water and over the land.

We are lucky that only two nuclear bombs have been used in the history of warfare so far but for the people of Japan, the emotional scars from the bombings of Hiroshima and Nagasaki may never be healed. Sadly, at least 129,000 people died in the bombings but the real death toll will never be known, as many more deaths resulted from radiation exposure and there are reports of many cancers and birth defects that may be linked to the effects of radiation as well.

In both cities most of those killed were civilians, leading to continuing international debate about whether or not these bombings were necessary to end the war. Many people consider the acts immoral, a war crime and even a form of terrorism. Contributors to Wikipedia offer an excellent debate over these concerns.

Why Nuclear Explosions Yield Much More Energy than Chemical Explosions

Why do nuclear bombs yield so much more energy than even the most powerful chemical bombs? It has to with the energy in the bonds that are broken during the reaction. Chemical explosions are chemical reactions in which only the atom's electrons are involved. Nuclear explosions involve bonds between protons and neutrons inside the nuclei of the atoms. To understand these differences, let's take a close look at the atom.

An atom consists of elementary particles called protons and neutrons, which are tightly bound within a nucleus. Outside the nucleus, the atom's electrons are found within orbital clouds.

The most realistic depiction of an atom is perhaps the orbital cloud model. A helium atom model is shown below. It consists of two protons, two neutrons and two electrons. The protons and neutrons, confined in the relatively very tiny nucleus, are shown as red and purple dots. The shaded grey disc shows us where electrons might be.

An atom is indeed tiny. 1 angstrom (Å) is 10-10 metres, or 100,000 fentometres
(10-15 m). The most powerful electron microscope today can barely "see down" to about 1 angstrom, the size of an atom.

In reality the electron cloud, left, would be spherical. The best mathematical model of the atom is the quantum mechanical model, which the left diagram is based on. It is defined by probabilities and uncertainty. The darkness of the cloud above represents the probability of finding an electron in a particular location within it. It's more likely to be close to the nucleus (darkest) than far away from it (lightest). The nucleus is very tiny compared to the atom's size.

An atomic model that is easier to conceptualize is the Bohr model. Bohr models of four small fairly simple atoms are shown below. This is the model that best helps us to visualize how chemical bonds between the electrons work.

Two kinds of bonds hold an atom together. Nuclear bonds hold protons and neutrons together in the nucleus. Electron bonds keep electrons bound to the atom. Each of these types of bonds is carried out by its own type of fundamental force, of which there are four. The strong force, aptly named, holds the nucleus together and the electromagnetic force holds the electrons in the atom. This is the force of electricity, magnetism and electromagnetic radiation including light. Inside the atom, the electromagnetic force is more specifically experienced as an electrostatic force: This is the force that makes opposite charges attract each other (think of static cling). The positive charges of the protons in the nucleus attract the negatively charged electrons to the atom.

The two kinds of energy associated with these forces are nuclear binding energy and electron binding energy, respectively. The difference in the energies associated with these two forces is the key to what makes nuclear explosions so much more powerful than chemical explosions. The strong force is 137 times stronger than the electromagnetic force. Let's look more closely at how these binding energies work inside atoms.

Chemical Explosive Energy Is About Chemical Bond Energy

We can describe two basic levels of chemical bonding. Atoms bind together to create molecules and molecules bind together to create larger molecules. An example of an atomic bond between two hydrogen atoms (H) to create hydrogen gas (H2) is shown below right. Each atom has one electron and these two lone electrons can share a single electron orbital. The energy payoff for doing so is that they create a more stable lower-energy system.

Jacek FH;Wikipedia

Molecules can also bind with one another. Below, two acetone molecules bond together (dotted line).
The hydrogen bond in hydrogen gas is an example of a covalent bond. This is the strongest class of chemical bond. The atoms are held together tightly and a fair amount of force is required to break them. The acetone-acetone interaction directly left depicts a dipole-dipole molecular interaction between two acetone molecules. Each molecule is an electric dipole. It has a more negatively charged region and a more positively charged region. Two oppositely charged regions of two molecules are attracted to each other. This is the weakest type of bond. You might know that acetone is a liquid at room temperature (some nail polish removers contain it). This bond is the reason why acetone is a liquid and not a gas. The bond is very weak however, so acetone readily evaporates. A similar dipole-dipole bond acts between water molecules. Water too is a liquid at room temperature and it evaporates, but not as fast as acetone does because its dipole-dipole bonds are stronger.

Chemical bombs are about chemical reactions, in which atomic and/or molecular bonds are broken and created. These bonds have potential energy, called bond energy. Like electrons attracted to a nucleus, chemical bond energy is derived from electrostatic interactions, and therefore the reactions involved in a chemical explosion fall into the electromagnetic energy scale.

The Unique Chemistry of Explosive Compounds

Although chemical bonds all fall under the electrostatic interaction umbrella, they vary widely in strength, from weak dipole-dipole interactions to ionic bonds (such as NaCl or table salt) to very strong covalent bonds. The nitrogen ≡ nitrogen triple (covalent) bond is the strongest chemical bond of all. This means that nitrogen gas (N2) (two nitrogen atoms triple bonded to each other) is, for the most part, chemically inert. It is non-reactive at room temperature and pressure, and it is challenging for living organisms and industry to access all the useful energy in those very strong stable bonds. However, once nitrogen atoms are liberated they will also bond very strongly with various other atoms, creating a variety of energy-rich molecules, some of which are explosive.

Explosive compounds tend to have two prerequisites: First, they contain very strong covalent bonds. For example, many explosive compounds contain either a nitro group (-NO2) or an azide group (-N3). A nitro group is shown below left. "R" simply depicts the rest of the (organic) molecule. The solid/dotted lines depict very strong nitrogen bonds in this group.

An azide group (the three N's) is depicted by the two resonant structures shown below right. "Resonant" means that, in reality, these two powerful nitrogen-nitrogen bonds exist in a hybrid state between the two structures shown.

Second, explosive compounds are unstable. Both azide groups and nitro groups are kinetically unstable, or labile. This means that, even though there are strong (stable) covalent bonds present, the three-dimensional structure of the molecule as a whole is not stabilized by those bonds. Rather than stabilizing the molecule, separate regions of strong positive and strong negative charges make it twisty and unwieldy. This means that these groups lower the activation barrier to the potentially explosive decomposition reaction (this process is covered in the previous article). That is why these compounds are sensitive to mechanical shocks or temperature change. A bump (as in the case of nitroglycerin, a nitro-group compound) can be enough to overcome the activation barrier, triggering an explosive decomposition reaction. A large amount of chemical energy from those strong covalent bonds is released very rapidly.

Nuclear Devices: Where the Energy Comes From

A key difference between a chemical reaction and a nuclear reaction is in how the reaction is conserved, or balanced. Balancing a nuclear reaction equation offers excellent clues about where the energy comes from.

First we will look at how chemical reactions are balanced. To balance a chemical reaction we need to make sure the numbers of different atoms on the reactant (left) side of the reaction equals the numbers of atoms on the product (right) side of the reaction equation. No atoms must be lost or created. The two TNT reactions from the previous article, shown below, are balanced. For example, there are 14 carbon atoms in the reactant and 14 carbons atoms in the products in both cases.

2 C7H5N3O6 → 3 N2 + 5 H2O + 7 CO + 7 C + energy
2 C7H5N3O6 → 3 N2 + 5 H2 + 12 CO + 2 C + energy

The number of atoms is always conserved and mass is always conserved in these reactions. Energy is also conserved in chemical reactions, although measuring it in a practical sense can be challenging for explosive reactions (we will get into this a bit more later on in this article). The energy of an explosion is chemical bond energy transforming into the mechanical energy of the shock wave, the kinetic energy of gases, other reaction products and debris, and the thermal energy, or heat, released by the explosion.

Mass-Energy Equivalence

For nuclear explosions, we need to revise the conservation rules. Mass and energy are not conserved (as separate entities!) in a nuclear explosion. Instead, mass is converted into energy. To understand how this works, we need to move a bit beyond the pre-quantum era of chemistry to take into account Einstein's equation, E = mc2. Energy equals mass x the speed of light squared. This equation tells us that there is an equivalent relationship between energy and mass. We can still talk about conservation of energy BUT we need to define energy in a broader sense. All mass, according to Einstein, has an equivalent energy associated with it. Perhaps even more surprising is the fact that most of the mass of atoms, molecules and objects comes not from the intrinsic masses of all the elementary particles inside them, but from energetic interactions between those particles. For example, the mass of a proton is many times higher than the masses of the individual quarks that make it up. The energy associated with the strong force binds quarks together into protons and neutrons, and this energy contributes much of the proton's mass. The strong force is carried out by a large and unknown number of massless particles called gluons inside the proton. A similar arrangement is thought to exist inside a neutron.

This mass-energy equivalence rule, an update from pre-quantum chemistry, also holds true for chemical reactions but the energies at play are too small to translate into any significant changes in mass during the reaction. In other words, although a chemical explosion reaction releases bond energy, bond energy does not significantly contribute to the mass of the molecules involved. Even for a tightly bound azide group, the potential energy present in the strong nitrogen bonds do not contribute significantly to its mass. I recommend that you read the second answer in the question I've linked to here. It offers great insight into the differences in mass-energy between chemical reactions, nuclear reactions and particle interactions inside colliders.

Residual Strong Force = Nuclear Binding Energy

Nuclear reactions involve energy associated with the powerful strong force, which is a very significant contributor of mass to protons and neutrons, while chemical reactions involve changes in electron orbital energies and energies associated with chemical stability. Atom-bound electrons simply have far less energy available than the energy that is tapped during a nuclear reaction. Nuclear explosions are direct evidence for the incredible amount of energy that is tied up inside the nuclei of atoms as the strong force. This mass-energy equivalence update allows us to use new conservation rules for nuclear reactions. In a chemical reaction, the numbers and types of atoms must not change, and we use this to balance our equation. In a nuclear reaction, they can and do change. With a few exceptions, we instead balance the numbers of protons and neutrons on each side of the equation, rather than the number of atoms. As we will see, in a nuclear reaction, atoms themselves change. In a nuclear reaction, thanks to mass-energy equivalence, we can also track how much energy is released by measuring the reduction in mass.

A nuclear reaction does not access all the strong force within an atom. Neutrons and protons remain intact so the strong force holding quarks together inside them is not involved. There is tremendous energy in a nuclear explosion but not even that amount of energy is enough to do that job. To blast protons or neutrons apart you need the highly focused ultra-intense energy available inside a high-energy collider.

Instead, a nuclear reaction depends on the much weaker but still very powerful residual strong force. This is a residuum of the strong force that holds the nucleons (protons and neutrons) together inside the nucleus. The energy in this residual force is what becomes accessible during a nuclear reaction.

A Closer Look at Nuclear Reaction Conservation Laws

Nuclear reactions come in many different types. Nuclear bombs rely on explosive fusion reactions and/or explosive fission reactions. Nuclear reactors rely on a much slower and highly controlled rate of fission (they are the subject of a future article in this series). Radioactive decay reactions (and there are many kinds or modes of decay) are spontaneous fission reactions. The Sun, for example, is a continuous fusion reaction, fusing hydrogen into helium. The reaction rate is controlled by the balance of two opposing forces - (inward) gravity and (outward) hydrostatic pressure. Despite their differences, all of these reactions follow three basic conservation laws: Invariant mass, charge and baryon number must balance for each side of the equation.

Conservation of Invariant Mass

Invariant mass is the rest mass of an object. For example, the invariant mass of a proton is approximately 1.67 x 10-27 kg (that's the mass of the quarks and the strong force mass contribution). Particle masses, tellingly, are more often measured in energy units, so we can also describe the proton's invariant mass as about 938 mega electron volts (MeV/c2) (almost 1 TeV or 1 tera electron volt; the c2 is usually dropped) of energy. Particle physicists find this measurement much more useful. The mass/energy of the protons and neutrons involved in the reaction is conserved. The numbers of protons and neutrons (with a few exceptions), as well as their individual masses, stay the same. With no exceptions, the total baryon number is conserved, as we will see.

Conservation of Baryon Number

Baryon number makes it possible for us to keep track of all the protons and neutrons in the atoms involved in our nuclear reaction so we can balance our equation. This is one of the most important conservation laws of nature. As we now know, every proton and neutron is made up of three fundamental particles called quarks. Each quark is assigned the baryon number 1/3. Any particle made of three quarks is called a baryon, so protons and neutrons (nucleons) are baryons or baryonic composite particles, and each nucleon has a baryon number of 1. A hydrogen atom with just one proton, therefore, has the baryon number 1 (it is called hydrogen-1). Lithium, with three protons and three neutrons in its nucleus, has the baryon number 6 (it is called lithium-6).

Reflecting the requirement of balancing baryon number, nuclear reactions are written a bit differently than chemical reactions. Below is an example of a nuclear reaction called deuterium-lithium fusion (which hasn't been balanced yet; this example reaction is borrowed from Wikipedia - find it at the link above).

When lithium-6 and deuterium (hydrogen-2) are forced together under very high pressure, they undergo a fusion reaction (deuterium  or hydrogen-2 is a stable isotope of hydrogen, containing 1 proton and 1 neutron). The trick with fusion reactions, and part of the challenge in designing a future fusion reactor, is that, while atoms can be attracted to one another and react chemically, the atomic nuclei deep inside them do not interact under ordinary conditions. In fact, two (positively charged) nuclei will repel each other very strongly (this is called the Coulomb barrier) if they are forced close together. That is, unless they get close enough to come under the influence of each other's residual strong force. This is the force that ultimately fuses the two nuclei into one. Only extremely high temperature and/or pressure, such as deep inside the Sun, will force two nuclei close enough to fuse.

A note here: deuterium-lithium fusion is simply a sample problem. Although the fuel of the hydrogen bomb (also called H-bomb or thermonuclear weapon) is solid lithium deuteride, the explosive reaction itself is a deuterium-tritium fusion reaction, not shown here. Tritium (hydrogen-3) is an unstable isotope of hydrogen containing two neutrons and one proton. The primary fission part of the H-bomb releases neutrons that split lithium-6 into tritium and helium-4. The tritium then fuses with deuterium during the secondary fusion part of the bomb to create more helium-4.

Back to our sample equation, now we can balance it.

For the lithium atom, 6 is the mass number, which is the number of protons and neutrons in the atom. Because each proton and neutron has a baryon number of 1, mass number is equivalent to the baryon number. 3, below, is the atomic number, the number of protons in the lithium atom. Li is lithium's chemical symbol. We know that baryon number must be conserved in this reaction, so what is our missing product? It must have a baryon number 4 so it could have any combination of neutrons and protons and still observe baryon conservation. Only one stable nucleus fits, with a stabilizing balance of neutrons and protons, and that is another helium-4.

This reaction is called a fusion reaction because lithium and deuterium fuse into an excited and highly unstable beryllium-8 nucleus (not included in the reaction above). This nucleus (the large central vibrating mass below) lasts only 7 x 10-17 seconds before it decays through alpha decay into two very stable helium nuclei, shown below.

Not all nuclei are stable. Nuclear decay is the process in which an unstable nucleus changes into a more stable nucleus. An unstable nucleus has either too many protons or too many neutrons. Because it is unstable, it contorts and vibrates and has too much internal energy. A stable nucleus is in a lower energy state. The unstable nucleus must lose energy in order to change (a process called transmutation) into a stable one. An unstable nucleus eventually stabilizes by ejecting an alpha particle or a neutron, or one of its protons can change into a neutron or vice versa. The emission of the high-speed helium nuclei (alpha particles) above is an example of alpha emission. The unstable beryllium-8 nucleus decays through alpha decay into two alpha particles. During the process, other particles such as electrons may be emitted, as well as electromagnetic radiation (not shown in the above reaction).

What Radiation Is and Where It Comes From

This nuclear reaction happens to conserve atomic number as well as baryon number, but not all do. Two kinds of decay reactions - beta minus decay and beta plus decay - do not conserve atomic number. These reactions, by changing the number of protons in an atom, change the identity of the atom.

Here is a helpful rule of thumb: Changing the number of electrons creates a charged atom or ion, changing the number of neutrons creates a different isotope of an atom, changing the number of protons changes an atom into a different atom.

When atomic nuclei are split open (fission) or fused, very high energies are involved. These fission and fusion reactions not only create products that we can expect when we balance an equation, such as the two helium nuclei in the example above, but the energy released may high enough to allow the creation of altogether new particles as well. These particles include electrons, positrons (the electron's antimatter twin), and neutrinos. However, even the most powerful H-bomb doesn't have enough energy to create new neutrons and protons. Very high-energy (very fast) helium nuclei are called alpha particles. Very high-energy electrons are called beta particles. A nuclear reaction can create alpha, beta or free neutron (particle) radiation, as well as gamma, X-ray and infrared (heat) electromagnetic radiation (EM). This radiation carries off some of the energy released in the explosion. In addition, a nuclear explosion creates a blindingly bright flash - this is EM radiation in the visible wavelength range.

Beta Radiation From Nuclear Reactions

To understand beta radiation, we'll look at two examples: carbon-14 and magnesium-23.

Carbon-14 is a slightly unstable atom. It will eventually transmute into stable nitrogen-14 through beta minus decay, emitting an electron (e-) and an electron antineutrino. This electron has high velocity so it is called beta radiation. The antineutrino is harmless as all matter, even Earth, is invisible to neutrinos - they just pass right through it.

Magnesium-23 is unstable too but it transmutes into stable sodium-23 through beta plus decay instead, emitting a positron (e+) and an electron neutrino.

Positron radiation is considerably more dangerous than beta radiation, even though the two particles have similar energies. As soon as the positron comes close to an electron (and electrons are everywhere in all matter) the matter/antimatter pair will annihilate into energy in the form of two gamma rays. Unlike beta radiation, gamma rays have enough energy to penetrate right through the body's tissues, including bone, to damage cells and DNA. Only thick shielding such as lead can stop them. Beta particles can only penetrate skin-deep.

In both of these reactions, baryon number is conserved but atomic number is not. A neutron in carbon-14 decays into a proton, creating a stable nitrogen nucleus. A proton in magnesium-23 decays into a neutron.

Beta plus decay poses an interesting puzzle. This reaction might seem impossible when we consider than a neutron has just a bit more mass than a proton does. How does the reaction gain mass? This is not an endothermic reaction, meaning that it does not absorb energy from the environment. The answer is that a proton inside an unstable nucleus has binding energy at its disposal, which it uses to decay into a neutron. A very small amount of mass is gained but the system moves into a more favourable lower energy state. This reaction mechanism is impossible for an isolated proton, and current understanding is that isolated protons are stable. If there is any instability it is miniscule, with an estimated half-life of about 1032 years, far longer than the lifetime of the universe.

Radiation From Fission And Fusion (Hydrogen) Bombs

Both types of beta decay occur after a nuclear fission bomb detonates, as various radioactive fission products decay into more stable atoms. Some of this decay is rapid, on the scale of milliseconds, while other decays will happen much more slowly. For example, strontium-90 is an unstable isotope within nuclear fallout. It has a half-life of 28.8 years as it decays through beta minus decay into stable yttrium-90. It is very hazardous because it acts like calcium in the body when it's ingested, being deposited in bone where its presence can cause bone cancer. The cancer is caused by a continuous dose of beta radiation (high-speed electrons) emitted by strontium-90 as it decays.

A note on half-life: Half-life means that, for strontium-90 for example, on average, half of a given sample will still be strontium-90 after 28.8 years and half will have decayed into yttrium-90. Decay is a probabilistic process. When an individual atom will decay is totally random. This is why strontium-90 delivers continuous radiation. It doesn't all decay at one time.

One might guess that a hydrogen bomb, which operates by fusion, does not create any radioactive fission-product fallout. However, all known fusion bombs have two parts, one of which creates the fission reaction that sets off the fusion explosion. The fission reaction, like fission weapons, creates various radioactive products. As well, the fusion reaction itself creates some radioactive tritium (a beta radiation emitter), but even more deadly is the fusion reaction's tremendous output of radiation, which includes neutrons, gamma rays, X-rays as well as alpha and beta particles. Furthermore, a hydrogen bomb detonation close to the ground can activate atoms in the soil, etc. Through intense neutron radiation, a wide variety of radioactive isotopes can be created. This radiation induces radioactivity when atomic nuclei capture free neutrons, become unstable themselves and emit gamma rays and beta radiation and possibly more alpha and neutron radiation.

Calculating the Explosive Energy of Chemical Versus Nuclear Reactions

We know that the fusion reaction in the Sun releases a tremendous amount of energy, and we can assume that the deuterium-tritium fusion reaction inside the H-bomb also releases a lot of energy. We aren't dealing with the chemistry of chemical bonds, so how do we calculate the energy released in a nuclear explosion?

A bomb calorimeter, for example, can accurately measure the heat of combustion reactions, those that deflagrate (explored in the previous article). It does this by measuring the reaction's enthalpy. It measures the initial and final temperature and measures the masses and specific heat capacities of the reactants. For explosive chemical reactions, a bomb calorimeter isn't as accurate. Products of the explosion, after everything is cooled back to room temperature, are usually not those present at the moment of maximum temperature and pressure. Therefore, explosive energy output is most often calculated indirectly instead, either by carrying out a performance test tailored to the type of explosive or by calculating an estimate of its explosive power by taking into account the reaction's oxygen balance (described in the previous article), the heat of explosion of the reaction, the volume of products and the chemical potential of the explosive.

A Sample Calculation

Like chemical explosions, the energy output of nuclear explosions can only be indirectly measured. Fortunately we can utilize Einstein's mass-energy equivalence. Once again we will use the lithium-deuterium reaction as our example. We can get an accurate measurement of the energy released simply by comparing the invariant mass on the left side with the right side of the equation:

For this, we can look up the relative atomic masses (u) of the reactants and products. The value u is the average mass of the atoms of an element. It is useful because many elements found in nature consist of a mixture of different stable isotopes, and we can simply look it up for any element on Wikipedia and elsewhere. Relative atomic mass therefore gives us a mass that reflects that element's composition in nature.

6.015 u (lithium) + 2.014 (hydrogen-2) = 8.029 u

8.029 u is the mass that would balance this reaction if we treated it like a chemical reaction. However, when we calculate the mass of our two helium nuclei products, we get less mass:

2 x 4.0026 (helium-4) = 8.0052 u

8.029 - 8.0052 = 0.0238 u

This is the mass equivalent of the energy that is created per one atom each of lithium and deuterium during this reaction.

One atomic mass unit (u) is defined as 1/12 the mass of a carbon-12 atom which equals 1.66 x 10-27 kg. This is the average mass of a nucleon (proton or neutron). We'll take this as the mass per 1 u. Now that we can translate u into mass in kg, we can use Einstein's equation to find out how much energy that's equivalent to:

E = mc2 so E = 1u x c(speed of light)2

E = (1.66 x 10-27 kg) x (3 x 108 m/s)2

E = 1.5 x 10-10 kg(m/s)2

This is the formulation of a unit of energy called the joule (J):

E (per u) = 1.5 x 10-10 Joules

We can translate this energy into electron volts. 1 MeV (mega or million electron volts) equals 1.6 x 10-13 J

E = 1.5 x 10-10 Joules x 1MeV/1.6 x 10-13 J = 931 MeV of energy released per u.

Now we can figure out what the explosive yield of our reaction is per kilogram of reactant mixture:

To get our answer into joules/kg:

We can take 1.5 x 10-10 J/u and divide by 1.66 x 10-27 kg/u to get 90 x 1015 J/kg (or 90 PJ/kg). However, just a tiny portion of the expected product's mass is converted into energy. The easiest way to get that is to take a percentage of the product mass than went missing. We know this went to energy:

0.0238 u/8.029 u = 0.003 or 0.03%
90 PJ/kg x 0.03% = 3 x 1014 J/kg or 300 TJ/kg

The energy output of this reaction is 300 TJ/kg. To put this in perspective, one kg of TNT releases 4.2 x 109 joules of energy. Let's compare the two:

3 x 1014 J/kg divided by 4.2 x 109 J/kg = 7.14 x 104 

This means that the fusion of one kg of lithium-deuterium releases 70,000 times more energy than one kg of TNT. This doesn't mean that if you put lithium and deuterium together they will spontaneously explosively fuse in a monumental explosion. What triggers a nuclear explosion and how the rates of nuclear reactions are controlled is the subject of the next article in this series.


Mass and energy are equivalent. Mass is converted into energy during a nuclear explosion. The speed of light squared in E = mc2 means that enormous energy is locked up in a tiny amount of mass. The total number of nucleons does not change during a nuclear reaction.

The energy of the reaction comes from nuclear binding energy, which contributes significant mass to atoms. Nuclear binding energy is the residual energy of the strong force that holds quarks together inside each nucleon. These reactions bring home the fact that mass and energy are two sides of the same coin, a fact that was unknown before Einstein.

Nuclear reactions tap a source of energy that is unavailable to chemical reactions which involve only the electrons of the atoms and the associated electromagnetic force, a much weaker fundamental force.

In the next article, we will explore in greater detail how nuclear binding energy works and how fission and fusion reactions are triggered and controlled.


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