Radioactivity II

***Radioactivity II*** is the fifteenth lecture within the **Properties of Matter** subtopic of PH1011. It covers the units that radiation is measured in, how radio carbon dating works and how exactly decays occur.

Previous: Radioactivity I

Next: Energy From Atoms I

## Content

### Units of Radiation

The rate of radioactive decay is measured in Bequerels (Bq). 1 Bq is 1 decay per second.

The absorbed dose, *D*, is the total amount of radiation taken in by a mass of tissue. This is measured in Grays, Gy, and is given by energy/mass (J/kg). But as radioactive damage is dependent upon the type of radiation absorbed, the quality factor *Q* must be taken into account - alpha particles have Q = 20, but beta and gamma radiation have Q = 1. These give the dose equivalent, H; measured in Sievert, Sv, H is given by ***H = Q x D***

### Sources of Radiation

Radioactive exposure stems from a variety of sources - it occurs both in nature and artificial scenarios. Artificially this is operations involving xrays, nuclear fuel, and some occupations involving radiation. Naturally, people are exposed to radiation from the atmosphere (incoming rays from space and the sun) and background radiation ccurring in areas with higher concentrations of radon in the air and/or uranium in the ground.

### Radio Carbon Dating

As before,

* ***N = N0e-λt***
* ***t0.5 = ln(2/λ)***

The ages of samples can be calculated if N0 is known and the current radioactivity is measured. In carbon dating, this is facillitated by the existence of the radioactive isotope <sup14C - cosmic rays supply incident neutrons to nitrogen in the atmosphere, forming heavy carbon atoms at a regular rate. All living things take in carbon-14 over their lifetimes at a regular rate through the photosynthesis of CO2 in plants an subsequent consumption of said plants by animals. Once the creature dies, its intake of carbon-12 ceases - and therefore measuring the number of 14C atoms present can show the age of a sample.

Radioactive dating can also be carried out with other isotopes to find the ages of non-organic materials, and relative abundances of isotopes with differing half lives can be used to find sample ages.

* **Example question:** A body of mass 70kg is found to be emitting 1000Bq. How old is it?
* Assuming that a body is 20% carbon, and of that carbon 14C exists in a ratio of 10-12, the number of carbon atoms present at time of death is given by -
* **No atoms = (mcarbon/Mcarbon x ratio x NA)**
* = ((0.2x70kg)/0.12kg mol<sup<-1) x 10-12 x 6.022x1023mol-1
* = 7x1014 atoms
* The decay rate λ can be calculated, knowing that the half life of carbon-14 is 5730 years (1.807x1011 seconds)
* λ = ln2/to
* = 3.8x1012 s-1
* The number of counts at time of death would be -
* 7x1014atoms x 3.8x1012counts per atom per second
* = 2660 counts per second
* As the count rate presently is 1000 counts per second,
* 1000 = 2660 exp(-3.8x10-12*t*)
* t = [ln(1000/2660)]/-3.8x10-12
* = 2.6x10-11
* = 8177 years

### Decay Mechanism

The half life of a sample is based on the probability of individual particles tunnelling out of the nucleus. This probability depends on the distance through which the particle must tunnel - the potential function is similar to the Lenard Jones Potential, but due to the nuclear force rather than electrostatic. When these particles exist the nucleus, they have an associated disintegration energy, which occurs due to mass conversion (see next lecture; total mass before decay > total mass afterwards, leaving E = mc2 to occur).

## Summary

Radiation is measured in Bq; counts per second. Dose is measured in Gy; energy per mass. Equivalent dose is measured in Sv; dose \* quality factor. Alpha particles have a quality factor of 20 whereas the other two have 1. Carbon dating is feasible as organic life takes in carbon-14 over its lifetime, which then decays steadily after death. Radioactive decays occur based on a potential function dependent upon the tunnel distance.