Energy From Atoms II

***Energy From Atoms II*** is the seventeenth lecture within the Properties of Matter subtopic of PH1011. It covers the role of neutrons and control in chain reactions, the difference between nuclear power plants and bombs, and the calculation of energy obtained from nuclear fuel.

Previous: Energy From Atoms I

Next: Subatomic Particles

## Content

### Energy from fission and the value of *k*

Fission is the splitting of a high mass atoms into several lower mass atoms via neutrom bombardment. This releases energy, for example:

1n + 235U => 141Ba + 92Kr + 3x 1n + ~200MeV

This is one fission path of uranium. Uranium exists in several isotopes, of which only 235U is unstable enough to decay on its own - therefore in nature it rarely does much damage, as neutrons emmitted are absorbed by surrounding 238U with no consequence. If the aim is to produce energy through radiation then 235U must exist in a more pure form (in power stations, samples are often 3-5% 235U; in nature it is only 0.7%) - as fission releases an average 2.4 neutrons, this can easily become a chain reaction which is self sustaining.

If the number of neutrons released that can then cause a subsequent fission is given as *k*:

* When *k* < 1, due to neutrons escaping or being absorbed (as is usually the case) the reaction is unsustainable and must have external neutrons input to allow it to continue.
* When *k* = 1, the reaction is perfectly self-sustaining.
* When *k* > 1, the reaction is described as run-away; it releases a large amount of energy very quickly, as reactions occur with an exponential rate until the sample has completely decayed.

### Nuclear power stations

Ideally a power station would operate at *k* = 1. They are fuelled by enriched uranium (slightly higher concentration of 235U than natural), and use moderators - compounds with light nuclei that do not readily absorb neutrons, but rather cause them to collide until they lose kinetic energy, eg graphite or D2O - to slow the neutrons enough that 235U can absorb them. Control rods allow moderation of how many neutrons are present - made of a material such as boron or cadmium that can absorb neutrons, these can be lifted or lowered between the fuel rods to cause faster or slower reactions. Coolant is present around the rods in order to transfer the energy produced to a heat exchanger, in order for it to reach a secondary cooling circuit. The second circuit is free from radiation and drives a turbine, which converts the energy into useful electricity. Coolants can be liquid sodium, CO2, boiling water or pressuried water depending on what type of reactor they're being used in. The latter two are useful as water can act as a moderator in addition to being a coolant.

**Example question:** Calculate the energy released in kWh from fission of one gram of 235U, assuming 200MeV per fission.

* E = number of atoms x energy per fission /energy in 1kWh
* = (1/235g mol-1x6.022x1023mol-1 x 200x106eV x 1.6x10-19 JC-1) / (3600 sh-1 x 1000W kW-1)
* = 22700 kWh

### Nuclear weapons

If *k*>1 for an extended eriod of time then an explosion will occur - this is the basis for nuclear weapons. Moderators are not necessary where a compact mass of 235U exceeds 50kg; two subcritical masses can be placed together to meet this critical mass and cause an explosion. This releases a huge amount of energy almost spontaneously.

Hydrogen bombs are different - they rely on fusion rather than fission energy. To achieve fusion, however, a fission must occur first - eg a nuclear bomb ("primary") is used to provide the energy to set off the hydrogen bomb. For example - neutrons can strike Li2, which allows fusion of the product (tritium) with the freed deuterium. This realeases energy approximately equivalent to 1MT of TNT.

## Summary

Fission of uranium-235 is often self-sustainable, and can therefore be used as an efficient energy source in power plants. It can however be used to produce a runaway reaction, causing huge amounts of energy to be released very quickly. This can be used to damage things straight up or to ignite a fusion bomb.