A-level Physics (Advancing Physics)/Risks, Doses and Dose Equivalents

Risk
Radioactivity results in risk - this could be a risk of death, or a risk of developing cancer. In physics, risk is what you expect, on average, to happen:

$$\mbox{risk} = \mbox{probability} \times \mbox{consequence}$$

So, if there is a 1 in 500 chance that someone gets run over by a car when crossing the road, the risk involved in allowing 500 people to cross the road is one accident.

Absorbed Dose
Absorbed dose is measured in grays, commonly denoted Gy. One gray is defined as one joule absorbed per kilogram.

The equation for absorbed dose (A.D) is:
 * $$ A.D = \frac{E}{m}$$

where
 * E is the energy given off by the source
 * m is the mass of the affected thing.

You may be expected to use the equation
 * $$E = hf = \frac {hc} {\lambda}$$

where
 * h is the Planck constant
 * f is the frequency of the photon
 * c is the speed of light
 * λ is the wavelength of the photon

or
 * $$E = ne$$

where
 * n is the number of particles
 * e is the magnitude of the charge of one electron

to calculate absorbed dose in terms of numbers of particles with a given frequency, wavelength or energy (in eV). If someone is exposed to a certain activity (particles per second) over a period of time, the absorbed dose accumulates.

Dose Equivalent


Absorbed dose does not give a full picture of the potential harm radioactivity can do to you. Different types of radiation do different amounts of damage. Absorbed dose equivalent, measured in sieverts (denoted Sv) attempts to compensate. To calculate the dose equivalent, multiply the dose in grays by the quality factor of the particles absorbed. These quality factors are given in the table below.

The equation for the effective dose (E.D) received is:

$$ \mbox{Effective Absorbed} = \mbox{Absorbed Dose} \times \mbox{quality factor}$$

Questions
1. A mobile phone emits electromagnetic radiation. 1.2 watts of power are absorbed per. kilogram. Assuming that the radiation is absorbed uniformly across a 5 kg head, what dose of radiation would be delivered to the head when making a 10-minute telephone call?

2. What dose equivalent does this correspond to?

3. How many nuclei are there in 1 mg of Americium-241?

4. A ham sandwich becomes contaminated with 1 &mu;g of Americium-241, and is eaten by an 80 kg person. The half-life of Americium-241 is 432 years. Given that Americium-241 gives off 5.638 MeV alpha particles, how long would it be before a dose equivalent of 6 Sv is absorbed, making death certain?

5. What assumptions have you made?

/Worked Solutions/