Nuclear Physics and Bombs

Topics

Elements and atoms Radioactive decay of atoms Fission and fusion Nuclear energy Nuclear bomb designs Nuclear explosion phenomena The Big-Bang theory

Basic Knowledge about Atom

The smallest particle (10-10 m or 0.1 nm) of an element that still retains the characteristics of the element.

An atom has a very small size (10-15 m) nucleus surrounded by negatively charged electrons.

Nucleus consists of protons (positively charged) and neutrons.

Proton and neutron have about the same mass that is very larger than electron’s. So an atom's mass is essentially the mass of its nucleus.

Periodic Table

– The number of protons (the atomic number) determines which element it belongs to. Atoms with the same atomic number but different number of neutrons are called isotopes, e.g., 235U and 238U.

Our Universe:

92% H; 7% He

Most abundant elements in the Earth: O, Mg, Si, Fe

Most other light elements have

escaped.

Peak at iron.

Radioactive Decay of Atoms Some elements will spontaneously turn into other elements.

This is called radioactivity and was discovered in 1896. It happens randomly and the probability only depends on the

structure of the nucleus (isotope). Scientists use half-life to describe the probability of decay.

Radioactivity Example

Example: 238U 206Pb + 8 4He + 6ß The half-life T1/2 of 238U is about 4.5 billion years.

The graph shows the number of 238U and 206Pb at time t

0

50

100

150

200

250

300

0 2 4 6

Time in half-life

Number of Atoms N238(t) = N0/2 t/T

N206(t) = N0-N238(t)

Radioactive Dating

This can be used in the opposite way: if we can count how much daughter isotope in the sample as compared to the parent isotope we can get the age of the sample t = T log2 (206Pb/238U + 1)

This method is called radioactive dating.

By using it, we find that Earth is ~4.5 Ga old.

0

5

10

15

20

25

30

35

40

0 2 4 6

Time in half-life

Ratio

206Pb/238U = 2t/T - 1

Fission ProcessHeavy elements are split into lighter ones.

Fusion ProcessLight elements are combined into more heavy ones

Nuclear Energy

Nucleons in the nucleus are bound tightly together by the so-called “strong force”. The nuclear binding energy is the energy required to break them apart. Therefore it is possible to release large amount of energy by breaking an nucleus to form a different nucleus that is bound more tightly, i.e., has higher binding energy.

Nuclear EnergyThe left figure shows the binding energy per nucleon of different atoms.

Iron is the most stable element.

Large amount of energy (yield) is released by fusion of light elements into heavier elements or by fission of heavy elements into lighter elements.

Yield of a 50 kg Uranium Bomb?

Fission of one 235U atom releases energy of 235 * 1 MeV/nucleon = 3.8 10-11 J.

235 gram of 235U has 6.0 1023 atoms (Avogadro’s number). A 50 kg U-bomb has a yield of 50,000/235*6.0 1023*3.8 10-11 = 4.8 1015 J.

The yield of 1 kt of TNT is 4.2 1012 J. So the yield of the 50 kg nuclear bomb is 1100 kt.

The first Uranium bomb, the Little Boy, is ~15 kt. The first generation A-bombs are not efficient.

US electric power consumption is about 3 1018 J in 2000.

Chain Reaction For 235U and 239Pu, one fission takes one neutron

and produces three neutrons on average. The produced neutrons can be used to split more 235U and start a chain reaction.

Nuclear Power Plants and Bombs

To sustain the chain reaction, it is necessary to have many fissionable atoms around to catch neutrons. The smallest amount of fissile material is called critical mass.

The critical mass depends on the density of the material and how easy for 235U to capture a neutron.

Inside a nuclear power plant, the reaction is controlled by absorbing neutrons and moderating their speed. Slow neutrons can be captured more easily so nuclear power plants can use low-grade uranium (a few per cent in 235U) as fuel.

In contrast, nuclear explosions are uncontrolled chain reaction. The fission material need to be supercritical and high grade (enriched).

The minimum mass is 47 kg for 235U and 16 kg for 239Pu in normal condition.

The mass can be reduced substantially by using tamper and increasing material density (e.g. the Fat Man bomb only used 6 kg of 239Pu).

Fission Bomb Designs

A fission device:1. a subcritical

system that can be made supercritical quickly;

2. a strong neutron source to initiate the supercritical system.

Fission Bomb Designs

Fission Bomb Designs

Boosted weapon: a small amount of deuterium-tritium mixture is placed in the center of the sphere of fissile material.

When the primary explosion happens, it produces enormous pressure and temperature at the center. This causes the deuterium and tritium mixture to undergo fusion and releases lots of neutrons in the center of the fissile sphere, greatly increasing the overall fission energy release.

Boosting can increase yields by a factor of ten (400 kt).

Fusion

To achieve fusion enormous temperatures are required. It takes about 50,000,000 degrees to get deuterium (2H) to fuse with tritium (3H). The required temperatures are higher for heavier elements.

At present, it appears that only a fission device is capable to initial fusion in a H-bomb. Other technology, such as laser, may be possible.

Once started, the energy released by fusion will sustain the process if enough fusion material are available.

Thermonuclear Bomb

Material for Nuclear Bombs

Usable materials are 235U, 239Pu, 2H, and 3H. 235U is less than 1% in natural uranium. It can be

enriched by using gas-diffusion or gas-centrifuge. 239Pu is virtually nonexistent in nature and can be

obtained by bombarding 238U with neutrons in nuclear reactors.

2H can be enriched by conventional methods. 3H can be produced by neutron irradiation of

lithium.

Making a Nuclear Bomb

Making a nuclear bomb requires a high degree of competence in various disciplinary.

Given enough time and supply, any nation or group with competent people should be able to produce a crude, heavy nuclear device.

Delivery the weapon on a sophisticated platform is not easy. Nuclear tests are likely to be needed in order to reduce the size and weaponize.

Other possibilities are to steal or purchase existing nuclear weapons, technology, or experts.

Nuclear Explosion Phenomena

The explosion happens in micro-seconds. Can you use the nuclear physics you've learned to

explain what's happening here?

The forms of nuclear energy

The energy released in the fission/fusion reactions are in the forms of kinetic energy of particles (neutrons and other produced elements) and high-energy gamma rays (photons).

In the atmosphere, the particles collide with air molecules to raise the temperature to 10 million degrees (thermal energy)

Nuclear Explosion Phenomena Hot air radiates electro-magnetic waves in a wide

spectrum from infra-red to visible and to X and gamma rays (thermal radiation and EM pulse).

The EM waves travel at speed of light. The high temperature also causes the pressure of

the air around the explosion to increase to a million atmospheric pressure (bar).

The highly-pressured air expands at speeds larger than the sound speed and generates shockwave.

For atmospheric explosions, shockwave takes about 50% of the yield and thermal radiation 35%.

Nuclear Explosion Phenomena

The fireball rises through the atmosphere in the form of a “mushroom” cloud.

Radioactive products of the nuclear explosions deposit around the area.

Some enter the upper atmosphere with the plume and fall to the ground over a large area.

New Generation Weapons

Neutron bomb: enhance neutron radiation with minimum radioactive fallout and shockwaves.

Reduced radiation weapons (RRW): maximize the electromagnetic pulse to destroy electronic equipment.

“doomsday bomb”: It has been hypothesized to produce a Cobalt bomb (coat the outside a thermonuclear device with a tamper of Cobalt). Neutrons produced in the fusion reaction will change Cobalt to Cobalt-60, which is a very radioactive atom with a half-life of 5.6 years. Such a bomb with enough Cobalt may kill all life by spreading dangerous radioactive material over the world.

Where Are Elements Made? The light elements hydrogen and helium were created during the

Big Bang and the elements between hydrogen and iron can be fused together inside stars. Heavier elements form during massive stellar explosions called supernovae.

Fusion in Stars

Stars like the Sun were mostly made of H initially and have a temperature of ~107 K. So, H to He fusion reaction is going on in stars (main sequence).

How did it get started in the first place?

The Birth of a Star

As hydrogen clouds condense, pressure and temperature at the center increase. This lead to the ignition of H fusion.

The Fate of a Star

When most H is fused into He, fusion stops and and the star starts to collapse under gravity.

For stars with mass less than the Sun, they become brown dwarf and eventually end up as cold, dead bodies in space.

For stars like the Sun, the gravitational force can squeeze the center and make it hot enough to start fusion of He. Star starts to swell into a red-giant.

Elements from Li up to Fe are produced. Eventually all fusion fuel are burnt out. It

collapses to form a white dwarf.

Supernova

More Massive stars tend to explode in a supernova.

Elements heavier than Fe are produced in explosion.

A small central core remains to form a neutron star.

If the mass is is large enough, the core continue to shrink to form a black hole

The crab nebula

How Much Time Do We have?

The Sun is radiating energy at a rate of 4 1026 W.

It has a mass of 2 1030 kg (1H). The main fusion process in the Sun is

combining 1H to 2H, which releases 1.4 MeV of energy. The amount of H in the Sun can keep the fusion process last for about 10 Ga.

At a age of 4.5 Ga, the Sun is in its middle age (no crisis yet).