Период физического полураспада.

 

Важной характеристикой радионуклидов является время, за которое их число уменьшается на половину. Этот период времени называется “периодом полураспада” радионуклида. Период полураспада (T_1/2, имеет размерность единицы времепни) и константа распада (λ, имеет размерность обратную единице времени) связаны следующим соотношением:

T_1/2 = ln2/λ

 

где ln – обозначение натурального логарифма.

 

Выражение, описывающее изменение активности радионуклида (A) со временем t, имеет следующий вид:

A(t) = A(0)×exp(-ln2×t/T_1/2 )

где A(0) – начальная активность радионуклида, exp – обозначение экспоненты.

Величины T _1/2 для различных радионуклидов представлены в соответствующих справочниках.

 

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MODULE 4: RADIATION DOSIMETRY

Exposure

As explained in the previous module, when radiation interacts with matter, electrons are removed from atoms through the process called ionization. When the energy of the radiation is not strong enough, electron excitation (jumps from lower shells to upper shells) may occur. The excitation of molecules or breaking of molecular bonds can also occur, causing damage to living cells. When the energy of radiation is large enough to produce ionizations, the radiation is called ionizing radiation. Otherwise, it is called non-ionizing radiation.

When dealing with the interaction of gamma and X-rays in air, the term exposure is used. Exposure measures the electric charge (positive or negative) produced by electromagnetic radiation in a unit mass of air, at normal atmospheric conditions.

In the SI system of units, exposure is measured in X unit:

1 X unit = 1 C/kg air

where C is Coulomb, the SI unit for electric charge.

The average energy dissipated to produce a single ion pair in air is 34 eV. Since the charge of an electron is equal to 1.6x10 ^-19 C, an association can be established between an X unit and the energy measured in Joules, dissipated in 1kg of air. Hence, one X unit is equivalent to 34 J/kg.

Formerly, before the SI system was adopted, the unit of X-ray exposure was called the Roentgen (R). R was defined as the quantity of gamma or X-radiation that can produce ions carrying one statCoulomb of charge (of either sign), per cubic centimetre of air at 0 degrees Celsius and 760 mm Hg of pressure (1 atm).

1 R = 1 sC/cm^3

The stat Coulomb is the old unit of measure for electric charge. The relation between SI unit (C) and sC is 1C = 3x10 ⁹ sC. As mentioned above to produce an ion (electric charge of 1.6x10 ^-19 C) an average energy of 34 eV = 34 x 1.6x10 ^-19 J is required. Since the mass of one cubic centimetre of standard air is 0.001293 g, an exposure of 1 Roentgen corresponds to absorbing energy of 0.00877 J/kg in dry air.

With the above associations we can now establish the correspondence between X unit and R:

1 X unit = 3881 R

 

1 R = 2.58 x 10^-4C/kg

At a distance "d" from a point source of radiation, exposure follows an inverse square law, that is, when the distance increases by a factor "k", exposure decreases by a factor "k ² ").

Example: Exposure from a Cs-137 point source at 10 cm is 10 R. Find the exposure at 1 m. Answer: The distance between the Cs-137 source and the point at which exposure is determined to have increased 10 times. Therefore, the exposure at 1 m will be 100 (102) times less, i.e. 0.1R = 100mR.

Exposure is a very useful physical term because it can easily be measured. We just have to measure the charge produced by the radiation in air (or the electrical current, multiplied by time) to find out the strength of the electromagnetic field. The instruments used for this purpose are ionization chambers. Measurement results are usually expressed in R or mR.

Absorbed Dose

Although exposure from gamma or X-rays is easily measured in everyday life, we also deal with other types of radiation, like alpha, beta, or neutron. Additionally, we are also interested in the effects of radiation in other materials (like human tissue, for example) not only in dry air.

To measure the interaction of all types of radiation with any kind of material, the term absorbed dose is used. The units of measure for absorbed dose in the SI system is J/kg or gray (Gy). Named after Louis Harold Gray. A radiation field that deposits 1 Joule of energy in 1 kg of material has an absorbed dose of 1 Gy.

The old unit of measure for absorbed dose is rad (short for "radiation absorbed dose"). The relationship between the SI unit and the old unit is:

1 Gy = 100 rad

or

1 rad = 0.01Gy

There exists a relationship between absorbed dose in dry air and exposure.

As explained above, 1 X unit is equivalent to 34 J/kg or 34 Gy.

Therefore:

1 R 0.877 rad in air

and 1 R 0.00877 Gy in air

However, a more important relationship exists between absorbed dose and exposure in tissue (gamma or X radiation). For a standard compostion of muscle tissue, with mass and electronic density compared to standard dry air mass and electronic density, we have:

1 X unit = 1 C/kg air 37 J/kg tissue

For muscle tissue, a good "rule of the tumb" is obtained by combining the above formulae:

1 R 1 rad in muscle

and 1 R 0.01 Gy in muscle

Important deviations from this rule apear, especially at low energy, for gamma and X-rays in other types of tissues. Absorbed dose in bone tissue at low energy is more than in muscle, while it is less in adipose tissue.