# Activity (physics)

Physical size
Surname activity
Formula symbol ${\ displaystyle A}$
Size and
unit system
unit dimension
SI Becquerel T −1

The activity or rate of decay of a quantity of radioactive substance is the number of nuclear decays per time interval. The SI unit of activity is the Becquerel (Bq). 1 Bq corresponds to one core decay per second. An obsolete unit of measurement is the curie (Ci). The following applies: 1 Ci = 3.7 • 10 10 Bq. The usual symbol for the activity is . ${\ displaystyle A}$

In nuclear medicine , the activity of a preparation is measured in an activimeter before it is used .

## definition

In general, the number of radioactive atoms in a preparation decreases over time as a result of the decay process . The activity is defined as: ${\ displaystyle N}$

${\ displaystyle A (t) = - {\ frac {\ mathrm {d} N} {\ mathrm {d} t}} (t) \}$.

So it is a time-dependent quantity and proportional to the number . However, it can be constant if atoms of the same radionuclide are regenerated in equilibrium with the decay. ${\ displaystyle N (t)}$

## Decay constant and law of decay

Every radionuclide has a decay constant (lambda), which indicates the probability per time interval for the decay of a single atomic nucleus. Therefore, the activity of a sample of atoms at the time can be expressed as ${\ displaystyle \ lambda}$${\ displaystyle N}$${\ displaystyle t}$

${\ displaystyle A (t) = - {\ frac {\ mathrm {d} N} {\ mathrm {d} t}} (t) = \ lambda \ cdot N (t)}$ .

The law of decay follows from this

${\ displaystyle N (t) = N_ {0} \ cdot e ^ {- \ lambda t} \,}$,

where is the number of atoms at the time . Since the activity is proportional to the number of radioactive atoms in the preparation, it follows the same exponential law of decay: ${\ displaystyle N_ {0}}$${\ displaystyle t = 0}$

${\ displaystyle A (t) = \ lambda \ cdot N (t) = \ lambda \ cdot N_ {0} \ cdot e ^ {- \ lambda t} = A_ {0} \ cdot e ^ {- \ lambda t} }$.

There is a relationship between and the half-life${\ displaystyle \ lambda}$ ${\ displaystyle T_ {1/2}}$

${\ displaystyle \ lambda = {\ frac {\ ln 2} {T_ {1/2}}} \ approx {\ frac {0 {,} 693} {T_ {1/2}}} \,}$ .

## Specific activity

The activity related to a mass is called the specific activity . Two different sizes are referred to by this name:

• the activity per mass of the pure radionuclide
• or the activity per mass of the respective chemical element in natural isotopic composition.

The SI unit of measurement is in any case Bq / kg.

In individual cases, differently defined specific activities - activity per mass of the chemical compound or activity per mass of the given mixture of substances - can also be useful. Information about a specific activity therefore only makes sense if it is clearly stated which reference mass is meant.

Since the activity is proportional to the mass of the pure radionuclide, when referring to this mass, the specific activity does not depend on the time of measurement, but is a constant property of the radionuclide. ${\ displaystyle A}$

## Importance of activity in radiation protection

A relationship between the activity of a substance and the harmful effect on humans cannot be established directly. The rays from radioactive decay have very different toxic effects depending on their type and kinetic energy . The absorbed dose is given in the unit Gray . In order to be able to better compare them with regard to the harmful effect ( relative biological effectiveness ) on organisms, it is multiplied by a [radiation weighting factor]]; the resulting dose equivalent is given in Sievert units . Without knowing the type and energy of the radiation, only the doses given in Sievert can be compared with one another.

Under certain conditions (known radionuclide , known type of absorption, etc.), the dose conversion factor can be used to approximately calculate the dose equivalent from the activity of the substance absorbed.

## literature

Hanno Krieger: Fundamentals of radiation physics and radiation protection . Vieweg + Teubner, 2007, ISBN = 978-3-8351-0199-9

## Individual evidence

1. Krieger, see list of literature, p. 124
2. A. Wiechen, H. Rühle, K. Vogl: Determination of the mass-related activity of radionuclides. Federal min. for environmental protection, 2013, ISSN 1865-8725