**Absorbed dose** is defined as the amount of energy deposited by ionizing radiation in a substance. The **absorbed dose** is given the symbol **D**. The absorbed dose is usually measured in a unit called the **gray** (Gy), derived from the SI system. The non-SI unit **rad** is sometimes also used, predominantly in the USA.

Units of absorbed dose:

**Gray**. A dose of one gray is equivalent to a unit of energy (joule) deposited in a kilogram of a substance.**RAD**. A dose of one rad is equivalent to depositing one hundred ergs of energy in one gram of any material.

## Gray – Unit of Absorbed Dose

A dose of **one gray** is equivalent to a unit of energy (joule) deposited in a kilogram of a substance. This unit was named in honor of **Louis Harold Gray**, who was one of the great pioneers in radiation biology. One gray is a large amount of absorbed dose. A person who has absorbed a whole-body dose of 1 Gy has absorbed one joule of energy in each kg of body tissue.

**Absorbed doses** measured in the industry (except nuclear medicine) often have usually lower doses than one gray, and the following multiples are often used:

**1 mGy (milligray) = 1E-3 Gy**

**1 µGy (microgray) = 1E-6 Gy**

Conversions from the SI units to other units are as follows:

- 1 Gy = 100 rad
- 1 mGy = 100 mrad

The gray and rad are physical units describing the incident radiation’s physical effect (i.e., the amount of energy deposited per kg). Still, it tells us nothing about the biological consequences of such energy deposition in living tissue.

## Examples of Absorbed Doses in grays

We must note that radiation is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us, and it is a part of our natural world that has been here since the birth of our planet. In the following points, we try to express enormous ranges of radiation exposure, which can be obtained from various sources.

**0.05 µGy**– Sleeping next to someone**0.09 µGy**– Living within 30 miles of a nuclear power plant for a year**0.1 µGy**– Eating one banana**0.3 µGy**– Living within 50 miles of a coal power plant for a year**10 µGy**– Average daily dose received from natural background**20 µGy**– Chest X-ray**40 µGy**– A 5-hour airplane flight**600 µGy**– mammogram**1 000 µGy**– Dose limit for individual members of the public, total effective dose per annum**3 650 µGy**– Average yearly dose received from natural background**5 800 µGy**– Chest CT scan**10 000 µGy**– Average yearly dose received from a natural background in Ramsar, Iran**20 000 µGy**– single full-body CT scan**175 000 µGy**– Annual dose from natural radiation on a monazite beach near Guarapari, Brazil.**5 000 000 µGy**– Dose that kills a human with a 50% risk within 30 days (LD50/30) if the dose is received over a**very short duration**.

As can be seen, low-level doses are common in everyday life. The previous examples can help illustrate relative magnitudes. From biological consequences, it is very important to distinguish between doses received over **short** and **extended periods**. An “**acute dose**” occurs over a short and finite period, while a “**chronic dose**” is a dose that continues for an extended period so that a dose rate better describes it. High doses tend to kill cells, while low doses tend to damage or change them. Low doses spread out over long periods don’t cause an immediate problem to any body organ. The effects of low radiation doses occur at the cell level, and the results may not be observed for many years.

## Calculation of Shielded Dose Rate in grays

Assume the **point isotropic source** contains **1.0 Ci of ^{137}Cs** and has a half-life of

**30.2 years**. Note that the relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown below. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

About 94.6 percent decays by beta emission to a metastable nuclear isomer of barium: barium-137m. The main photon peak of Ba-137m is **662 keV**. For this calculation, assume that all decays go through this channel.

**Calculate the primary photon dose rate**, in gray per hour (Gy.h^{-1}), at the outer surface of a 5 cm thick lead shield. The primary photon dose rate neglects all secondary particles. Assume that the effective distance of the source from the dose point is **10 cm**. We shall also assume that the dose point is soft tissue and it can reasonably be simulated by water, and we use the mass-energy absorption coefficient for water.

See also: Gamma Ray Attenuation

See also: Shielding of Gamma Rays

**Solution:**

The primary photon dose rate is attenuated exponentially, and the dose rate from primary photons, taking account of the shield, is given by:

As can be seen, we do not account for the buildup of secondary radiation. If secondary particles are produced, or the primary radiation changes its energy or direction, the effective attenuation will be much less. This assumption generally underestimates the true dose rate, especially for thick shields and when the dose point is close to the shield surface, but this assumption simplifies all calculations. For this case, the true dose rate (with the buildup of secondary radiation) will be more than two times higher.

To calculate the **absorbed dose rate**, we have to use the formula:

- k = 5.76 x 10
^{-7} - S = 3.7 x 10
^{10}s^{-1} - E = 0.662 MeV
- μ
_{t}/ρ = 0.0326 cm^{2}/g (values are available at NIST) - μ = 1.289 cm
^{-1}(values are available at NIST) - D = 5 cm
- r = 10 cm

**Result:**

The resulting absorbed dose rate in grays per hour is then:

If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The **extended formula** for the dose rate is then: