# Radiation dosage

Various types of radiation including ionizing radiation may cause harm to people, researchers, and students under different situations.
This problem set is designed to help you calculate how much radiation and of what type you may be exposed to and how much damage it might cause.
The idea is forewarned is forearmed so that should you find yourself performing research requiring the use of radiation you will use proper and effective precaution.

## Radiation sickness

Def. any "illness produced by ionizing radiation with symptoms ranging from nausea through to death" is called radiation sickness.

## Dosages

Def. an "addition of a small measured amount of a substance to something" is called a dosage.
Def. a "quantity of an agent (not always active) substance or radiation administered at any one time" is called a dose.

## Dose equivalents

“The equivalent dose to a tissue is found by multiplying the absorbed dose, in gray, by a weighting factor (W$_R$). The relation between absorbed dose D and equivalent dose H is thus:
    $H=W_{R}\cdot D$.
The weighting factor (sometimes referred to as a quality factor) is determined by the radiation type and energy range.
    $H_{T}=\sum _{R}W_{R}\cdot D_{T,R}\ ,$
where
    H$_T$ is the equivalent dose absorbed by tissue T
    D$_{T,R}$ is the absorbed dose in tissue T by radiation type R
    W$_R$ is the weighting factor defined by the following table
| Radiation type and energy | Radiation type and energy | W$_R$ |
| electrons, muons, photons (all energies) | electrons, muons, photons (all energies) | 1 |
| protons and charged pions | protons and charged pions | 2 |
| alpha particles, fission fragments, heavy ions | alpha particles, fission fragments, heavy ions | 20 |
| neutrons (function of linear energy transfer L in keV/μm) | L < 10 | 1 |
| neutrons (function of linear energy transfer L in keV/μm) | 10 ≤ L ≤ 100 | 0.32·L − 2.2 |
| neutrons (function of linear energy transfer L in keV/μm) | L > 100 | 300 / sqrt(L) |
Thus for example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv. The maximum weight of 30 is obtained for neutrons with L = 100 keV/μm.

## Effective doses

The effective dose of radiation (E), absorbed by a person is obtained by averaging over all irradiated tissues with weighting factors adding up to 1:
    $E=\sum _{T}W_{T}\cdot H_{T}=\sum _{T}W_{T}\sum _{R}W_{R}\cdot D_{T,R}$.
| Tissue type | W$_T$ (each) | W$_T$ (group) |
| Bone marrow, colon, lung, stomach, breast, remaining tissues | 0.12 | 0.72 |
| Gonads | 0.08 | 0.08 |
| Bladder, oesophagus, liver, thyroid | 0.04 | 0.16 |
| Bone surface, brain, salivary glands, skin | 0.01 | 0.04 |
| total | | 1.00. |

## Gray

The gray (symbol: Gy) is the SI derived unit of absorbed radiation dose of ionizing radiation (for example, X-rays), and is defined as the absorption of one joule of ionizing radiation by one kilogram of matter (usually human tissue). The rad is equivalent to 0.01 Gy.
One gray is the absorption of one joule of energy, in the form of ionizing radiation, per kilogram of matter.
    $1\ \mathrm {Gy} =1\ {\frac {\mathrm {J} }{\mathrm {kg} }}=1\ \mathrm {m} ^{2}\cdot \mathrm {s} ^{-2}$
For X rays and gamma rays, these are the same units as the sievert (Sv). For alpha particles one sievert is twenty gray. To avoid any risk of confusion between the absorbed dose (by matter) and the equivalent dose (by biological tissues), one must use the corresponding special units, gray is used instead of the joule per kilogram for absorbed dose and the sievert instead of the joule per kilogram for the dose equivalent. The word "gray" is both the singular and plural spelling.

## Backgrounds

Def. "ionizing radiation that is naturally present in the environment" is called background radiation.
Background radiation is the ubiquitous ionizing radiation that the general population is exposed to, including natural and artificial sources. Both natural and artificial background radiation varies by location.
The worldwide average natural [effective radiation] dose to humans is about 2.4 millisievert (mSv) per year.
The biggest source of natural background radiation is airborne radon, a radioactive gas that emanates from the ground. Radon and its isotopes, parent radionuclides, and decay products all contribute to an average inhaled dose of 1.26 mSv/a. Radon is unevenly distributed and variable with weather, such that much higher doses apply to many areas of the world, where it represents a significant health hazard. Concentrations over 500 times higher than the world average have been found inside buildings in Scandinavia, the United States, Iran, and the Czech Republic.
Terrestrial radiation usually only includes sources that remain external to the body. The major radionuclides of concern are potassium, uranium and thorium and their decay products, some of which, like radium and radon are intensely radioactive but occur in low concentrations.
An average human contains about 30 milligrams of potassium-40 ($^{40}$K) and about 10 nanograms (10$^{−8}$ g) of carbon-14 ($^{14}$C), which has a decay half-life of 5,730 years. Excluding internal contamination by external radioactive material, the largest component of internal radiation exposure from biologically functional components of the human body is from potassium-40. The decay of about 4,000 nuclei of $^{40}$K per second makes potassium the largest source of radiation in terms of number of decaying atoms. The energy of beta particles produced by $^{40}$K is also about 10 times more powerful than the beta particles from $^{14}$C decay. $^{14}$C is present in the human body at a level of 3700 Bq with a biological half-life of 40 days. There are about 1,200 beta particles per second produced by the decay of $^{14}$C. However, a $^{14}$C atom is in the genetic information of about half the cells, while potassium is not a component of DNA. The decay of a $^{14}$C atom inside DNA in one person happens about 50 times per second, changing a carbon atom to one of nitrogen. The global average internal dose from radionuclides other than radon and its decay products is 0.29 mSv/a, of which 0.17 mSv/a comes from $^{40}$K, 0.12 mSv/a comes from the uranium and thorium series, and 12 μSv/a comes from $^{14}$C.
Background radiation may simply be any radiation that is pervasive, whether ionizing or not. A particular example of this is the cosmic microwave background radiation, a nearly uniform glow that fills the sky in the microwave part of the spectrum; stars, galaxies and other objects of interest in radio astronomy stand out against this background.
In a laboratory, background radiation refers to the measured value from any sources that affect an instrument when a radiation source sample is not being measured. This background rate, which must be established as a stable value by multiple measurements, usually before and after sample measurement, is subtracted from the rate measured when the sample is being measured.

## Problem 1

A gamma-ray burst has occurred somewhere nearby to Earth. The burst at maximum intensity lasted 100 s. While gamma-rays are absorbed by the Earth's atmosphere, conditions are such that where you are walking outside, you receive and absorb 10 % of the intensity over the 100 s.
The gamma-rays are at 1.8 MeV to the ground. The flux upon you is 4 x 10$^3$ photons · cm$^{-2}$ · s$^{-1}$ · MeV$^{-1}$.
What is your absorbed dose and your dose equivalent? Calculate your various effective doses and your dose rate.
Using the table below, describe your likely symptoms if any.
| Phase | Symptom | Whole-body absorbed dose ([Gray] Gy) | Whole-body absorbed dose ([Gray] Gy) | Whole-body absorbed dose ([Gray] Gy) | Whole-body absorbed dose ([Gray] Gy) | Whole-body absorbed dose ([Gray] Gy) |
| Phase | Symptom | 1–2 Gy | 2–6 Gy | 6–8 Gy | 8–30 Gy | Greater Than 30 Gy |
| Immediate | Nausea and vomiting | 5–50% | 50–100% | 75–100% | 90–100% | 100% |
| Immediate | Time of onset | 2–6 h | 1–2 h | 10–60 min | < 10 min | Minutes |
| Immediate | Duration | < 24 h | 24–48 h | < 48 h | < 48 h | N/A (patients die in < 48 h) |
| Immediate | Diarrhea | None | None to mild (< 10%) | Heavy (> 10%) | Heavy (> 95%) | Heavy (100%) |
| Immediate | Time of onset | — | 3–8 h | 1–3 h | < 1 h | < 1 h |
| Immediate | Headache | Slight | Mild to moderate (50%) | Moderate (80%) | Severe (80–90%) | Severe (100%) |
| Immediate | Time of onset | — | 4–24 h | 3–4 h | 1–2 h | < 1 h |
| Immediate | Fever | None | Moderate increase (10-100%) | Moderate to severe (100%) | Severe (100%) | Severe (100%) |
| Immediate | Time of onset | — | 1–3 h | < 1 h | < 1 h | < 1 h |
| Immediate | [Central nervous system] CNS function | No impairment | Cognitive impairment 6–20 h | Cognitive impairment > 24 h | Rapid incapacitation | Seizures, Tremor, Ataxia, Lethargy |
| Latent period | | 28–31 days | 7–28 days | < 7 days | none | none |
| Illness | | Mild to moderate Leukopenia Fatigue Weakness | Moderate to severe Leukopenia Purpura Hemorrhage Infections Epilation after 3 Gy | Severe leukopenia High fever Diarrhea Vomiting Dizziness and disorientation Hypotension Electrolyte disturbance | Nausea Vomiting Severe diarrhea High fever Electrolyte disturbance Shock | N/A (patients die in < 48h) |
| Mortality | Without care | 0–5% | 5–100% | 95–100% | 100% | 100% |
| Mortality | With care | 0–5% | 5–50% | 50–100% | 100% | 100% |
| Mortality | Death | 6–8 weeks | 4–6 weeks | 2–4 weeks | 2 days–2 weeks | 1–2 days |
| Source: |||||||
A few minutes after you've calculated your condition, a special report comes through an emergency channel on your cell phone to tell you that the initial report mentioned above was in error. The actual flux received whole body is 10$^6$ higher. Recalculate your situation and answer the above questions and calculations again. How are you doing? Will you live to get to Problem 2?

## Problem 2

Gamma-ray bursts are often followed by an X-ray afterglow. Even though you are at high altitude for some skiing when the gamma-ray burst occurred, there is probably more than enough atmosphere to prevent any further damage from the X-rays. The afterglow lasts for two days at only 5 % of the final flux of gamma rays at 120 keV. If the atmosphere had not been there, answer the questions and calculations of Problem 1 for the X-rays.

## Problem 3

This just isn't your day. On a separate military channel given to you by one of your Army buddies you find out that during the gamma ray burst about the same flux of protons and pions was received by you. Recalculate again and assess your condition. Do you need to know where the nearest hospital is?

## Problem 4

Oh, yes, this just keeps getting better and better. One of the people in your skiing group has a contact at the local hospital. She has just learned that alpha particles at a comparable flux were included behind the gamma-ray burst for a day and a half. Re-assess your situation again. Will you live long enough to try that new restaurant in town?

## Problem 5

A first aid worker was wearing a neutron detector and happen to fall ill near you. You glance at the detector and notice it has maxed out at L = 100 keV/µm. Before any of your fingers fall off you reassess your situation one last time. Are you still going to live?

## Hypotheses

* Additional approaches to radiation dosage can produce novel problems and problem sets.