9.1 Physical Quantities & Units

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In physical units we distinguish:

  • basic unit;
  • derived units;
  • multiple  and submultiple units;
  • sub-units.

Basic quantities and their units

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Derived quantities and units

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Derived units of MECHANICAL quantities

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Derived units of ACOUSTIC quantities

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Derived units of THERMAL quantities

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Derived units of MOLECULAR quantities

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Derived units of ELECTRIC quantities

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Derived units of OPTIC quantities

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Derived units of quantities in ATOMIC PHYSICS and RADIOLOGY

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9.1.1 Definition of quantities and units in RADIOLOGY

  • Activity

The basic variable in radiochemistry is activity. Activity A, body of a radioactive element (isotope), is defined as the ratio of the differential radioactive transformations of N and time t

BF Formula 1.png

The main unit is: 1 becquerel = 1 Bq = 1 reciprocal second = 1 s-1.

Former unit is: 1 curie = 1 Ci = 3.7 * 1010 Bq.

  •  Half-life (of conversion) (T1/2)

Half-life (half-life of conversion) T1/2 mean median length of time for which any initial quantity of homogeneous atoms (nuclides) radioactive decay spontaneously just half of this:

T1/2  is the mean median length of time which any initial quantity of homogeneous atoms (nuclides) take to radioactively spontaneously decay to just half of their initial volume/amount/quantity:

BF Formula 2.png

(where) λ denotes the radioactive decay constant of the reference sample.

  • Decay constant (λ)

Decay constant λ is understood as the variable characterizing the temporal instability of the radioactive element (isotope). It is the constant of proportionality between time (t) decrease in the number of atoms (N) radionuclide -dN/dt caused by spontaneous transformation, and the total number N of atoms of the same nuclide, which are still radioactively nondecayed. This begins with the time of the act of spontaneous radioactive decay and is defined as

BF Formula 3.png

Time-dimension is 1, then the reciprocal of the second unit, ie s-1.

Decay constant is a variable specific activity of the element relative to the total number N of nuclides in the sample. It is therefore also intended by the following formula:

BF Formula 4.png

Relationship with a median life indicates the relationship

BF Formula 5.png

Even in this context, recall the statistical validity of the law of decay

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where N0 is the number of atoms in the initial nondecayed time tracking, and N nondecayed loss after time t. Decay constant for the unit Becquerel (Bq) is not used, is intended solely activity and units derived from it.

  • Current density of particles

Particle current density J is the mean proportion of N particles that pass for some time t An a flat surface (perpendicular to the direction of motion of particles) and the size of the area and the time interval. In vector notation:

BF Formula 7.png

Unit is the reciprocal square meter per second, ie m-2s-1.

  • Linear attenuation coefficient

Linear attenuation coefficient μ is the mean rate of decline in current density 

J particle depends on the length of x in its path to the substance according to the relations:

BF Formula 8.png

The main unit of the linear attenuation coefficient is reciprocal meter, ie, m-1.

The inversion of the linear attenuation coefficient (1 / μ) thickness means a substance in which the current density particles are attenuated from the initial value to the value J0 = J / e ≈ 0.368 J0.

  • Half-thickness

Half-thickness d1/2 is the mean layer thickness reducing the current density J of particle beam to half its original value. For the exponential absorption

BF Formula 9.png

where μ is the linear attenuation coefficient. The layer thickness is the same in the direction towards the current density particles.

  • Mean lifetime

Mean lifetime of radioactive element τ means the average time necessary for the decreasing of the number N0 of atoms or nuclei of a species, which exist in a particular state to a number equivalent to the value of:

N = N0 / e

where e is the base of natural logarithms (e ≈ 2.718282). Size is 1 s.

  • The total flux of particles

Total particle flux (emission sources) Φp is the ratio of the number ΔN of particles emitted by a source and time t in which the particles passed through the selected area of ​​a certain size.

BF Formula 10.png

Dimension is time-1, the main unit is s-1.

  • Shutter speed

Shutter speed (exposure power, before irradiation also speeds) mean rate of change of X irradiation

BF Formula 11.png

where ΔX denotes the mean irradiance increasing in the time interval t. The main unit of exposure rate is ampere per kilogram, A .kg-1.