How small can a nuclear explosion be?

How small can a nuclear explosion be? Fission or fusion – a critical mass explosion is what I have in mind. I was half-watching Starship Troopers last night and they have these darling little nuke grenades that give off an explosion with a three metter cubed sized mushroom cloud.

If you can narrow it down to the number of atoms involved, the energy release in jules would be a fine and dandy answer.

Theoretically, every atom splitting or fusing is a ‘nuclear explosion’. I assume you mean with a bomb, meaning an uncontrolled chain reaction. In that case, the W54 artillery projectile (Better known as the “Davey Crockett”) is probably the smallest, with an adjustable yield from 1kt to as low as .01 kt. That’s 10 tons of TNT, which is only about twice as powerful as the Amphol bomb used by Timothy McVeigh in the Oklahoma bombing. Of course, there are radiation problems with a nuclear bomb, but still, this is pretty small. One could go off across the street from you and you could survive it.

One niggling point: There’s nothing special about a nuclear bomb in creating a ‘mushroom cloud’. Mushroom clouds form when energy is released in a large enough amount that the changing atmosphere itself affects the shape of the cloud.

In a large nuclear explosion, the initial blast forces a hot column of air upwards. As it rises, adiabatic expansion eventually causes it to cool and condense, creating a cloud. At first, thermal pressure from below causes it to shoot upwards, creating the stem of the cloud. Eventually, the bubble of hot gas slows down and starts to expand, again from adiabatic expansion. But because it’s no longer being forced upwards, it turns into a regular cloud, which is the ‘cap’ on the mushroom. If it travels high enough, it will encounter the jetstream, which will shear the top off, creating an ‘anvil’ shape familiar to anyone who’s seen a giant prairie thunderstorm.

If you could make a nuclear explosion the size of a firecracker, you’d get a firecracker-type cloud, which would differ only in the way the residue in the types of materials in the bomb is presented (much like different fireworks shells make different explosions based on the composition of the powder and impurities inserted into the powder to control burn temperature, color, etc).

So, while I don’t know exactly what a small nuclear explosion would look like, we know it wouldn’t create a room-sized mushroom cloud.

Taking this to a logical extreme, in his book The Making of the Atomic Bomb Richard Rhodes says that the energy released by the fission of one atom of uranium-235 is enough to make a grain of sand visibly jump.

That’s kind of dandy. I can look up the exact joules released for you if you are interested.

I thought an A-bomb went off automatically when the mass of U-235 or plutonium-238 reached critical mass.

Is critical mass so small it will go off at low enough levels to produce the mini-explosions you mentioned?

Or is it set off by the polonium triggers I vaguely remember reading about?

Any information you could provide would be appreciated.

Please consult the Nuclear Weapons FAQ at:

They have it divided into different design goals, lke minimum size, minimum fissile content, minimum yield. Here are the highlights:

“The absolute minimum possible mass for a bomb is determined by the smallest critical mass that will produce a significant yield. Since the critical mass for alpha-phase plutonium is 10.5 kg, and an additional 20-25% of mass is needed to make a significant explosion, this implies 13 kg or so.”

“The smallest nuclear weapons actually deployed have had yields around 10 tons (like the W54), and have been intended for short range tactical or nuclear demolition use (e.g. blowing up roads and bridges).”

Read that again carefully. I betcha he said that the energy released is EQUIVALENT to the energy required to make a grain of sand hop. I guarantee he never said you could make a grain of sand hop with one atom of U235.

You can have practically microscopic fusion explosions if you choose to. This is one method by which fusion researchers are seeking to produce economically viable fusion power. IIRC these involve a series of very small pellets of a deuterium/tritium compound which are blasted by powerful convergent lasers.

Now, basically, a nuclear reaction is when a netron splits a cell’s nucleus. This releases a whole lot of energy. Critical mass is when enough radiation is coming out of a large enough sample of, say, uranium 235, in a small enough area to split a whole lot of atoms to create a chain reaction. And it go boom-boom.

INERTIAL CONFINEMENT FUSION uses the principles of the hydrogen bomb (left), in which radiation from a fission bomb (called the primary) compresses and heats the fusion fuel, which is contained in the secondary. The minuscule laboratory equivalent (right) aims to bathe the peppercorn-size fuel pellet symmetrically in radiation and to concentrate the power into the pellet so that it implodes uniformly.

I don’t see why you couldn’t have a nuclear bomb with an arbitrarily small yield. If you limit your bomb reaction to fast, prompt fission (i.e. no moderator and no delayed neutrons), there’s a lower limit to the amount of fissile material needed for the bomb, but there’s no reason to require that all the fissile material react.

For example, you could fire a Uranium slug through a subcritical hollow cylinder of Uranium such that while the slug is passing through the cylinder the assembly is just barely supercritical. A neutron source could be attached to the slug. You could probably make such a device so that it only releases a few joules of thermal energy. Does that qualify as a bomb?

Fusion reactions aren’t generally chain reactions–the products of the reaction are not used in subsequent reations–so it’s harder to say what counts as a bomb.

I’m curious about the adjustibility of the Davy Crockett. I’m assuming that it carried the same warhead, but the timing of the conventional explosives used to trigger the reaction could be modulated to increase or reduce the efficiency of the reaction. But lowering the efficiency of the reaction should make a low-yield explosion extremely “dirty” (radioactive), shouldn’t it?

Efficiency is not a hallmark of nuclear weapons. Even the most nuclear fuel efficient bombs convert only a tiny fraction of their uranium into fissile products. The phenomenon of critical mass is one of statistical probability. If neutron emissions of normal, or enhanced decay products hit other nuclei often enough to sustain an increasing chain reaction, you get an explosion. How big an explosion you get, depends on how long that chain reaction continues.

A lot of factors affect the length of that reaction. How pure is the reaction material? How dense is it? How many neutrons are available from intermediate fission products and engineered sources, such as neutron enhanced environments? How much of the energy produced is captured as heat, and transferred to material in the near vicinity of the bomb. How refractory is the exterior construction of the bomb? You build your bomb to meet the criteria you want to meet.

The amount of (nuclear) material left over is very nearly the same as the amount of material you started with, although it tends to be spread out a bit. Some additional material will be transmuted to radioactive isotopes as well, but not really very large amounts, unless you have a ground burst designed to interact with a large volume of mass, or have deliberately encased the bomb in a material which absorbs neutrons readily.

The nuclear reaction part of the explosion is over long before you see the mushroom cloud. In fact, it is over before you even see the blinding flash. After that, it’s all just stuff getting out of the way.