Becquerel

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The becquerel or becquerel (symbol: Bq) is a unit derived from the International System of Units which measures radioactive activity. One becquerel is defined as the activity of a quantity of radioactive material with the decay of one nucleus per second. It is equivalent to one nuclear disintegration per second. The unit of Bq is therefore inverse to the second. For applications related to human health, this is a small quantity, and SI multiples of unity are commonly used.

It can be calculated by differentiating N with respect to time (t):

$A=frac{-dN}{dt}=lambda N; A=A_{0}e^{-lambda t}$

N being the number of radioactive nuclei without disintegration, $lambda$ the radioactive constant, characteristic of each isotope, and $A_{0}$ the activity in the initial moment.

It is named in honor of the French physicist Henri Becquerel who shared the Nobel Prize in Physics with Pierre Curie and Marie Skłodowska Curie in 1903 for their work in the discovery of radioactivity.

Name

The four forms becquerel, becquerelio, bequerel and becquerel (that is: with or without the suffix -io; with or without simplification of the -cqu- group, foreign to the Castilian orthographic system) exist in authoritative sources in Spanish. The International Electrotechnical Commission registers "becquerel" and "becquerelio". The RAE Spelling recommends "bequerel". as a crude foreign expression). Royal Decree 2032/2009 in Spain registers "becquerel". Nacional de Medicina, which also admits "becquerel" and "becquerelio".

Definition

1 Bq = 1 s⁻¹

Introduced a special name for the inverse second (s⁻¹) to represent radioactivity and avoid potentially dangerous mistakes with prefixes. For example, 1 µs⁻¹ would mean 10⁶ disintegrations per second: 1(10⁻⁶ s)⁻¹ = 10⁶ s⁻¹, while 1 µBq would mean a decay per 1 million seconds. Other names considered were hertz (Hz), a special name already used for the second reciprocal, and Fourier (Fr). Hertz is now only used for periodic phenomena. While 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radioactivity event per second.

The gray (Gy) and becquerel (Bq) were introduced in 1975. Between 1953 and 1975, absorbed dose was often measured in rads. Decay activity was measured in curies before 1946, and often in rutherfords between 1946 and 1975.

Caps and unit prefixes

As with all International System of Units (SI) units named after a person, the first letter of their symbol is capitalized (Bq). However, when the name of an SI unit is written in all letters, it must always begin with a lowercase letter (becquerel, becquerel) - except in a situation where any word in that position is I would capitalize, such as at the beginning of a sentence or in material that uses a title.

Like any SI unit, Bq can have the prefix; Commonly used multiples are kBq (kilobecquerel, 10³ Bq), MBq (megabecquerel, 10⁶ Bq, equivalent to 1 rutherford), GBq (gigabecquerel, 10⁹ Bq), TBq (terabecquerel, 10¹² Bq) and PBq (petabecquerel, 10¹⁵ Bq). Large prefixes are common for practical uses of the unit.

Relationship with curium

The becquerel (becquerel) has succeeded the curie (Ci), an older unit of radioactivity that is not part of the SI. Curium is based on the activity of 1 gram of radium-226. The curie is defined as 3.7×10¹⁰ s^-1, or 37 GBq.

Conversion factors:

1 Ci = 3.7 · 10¹⁰ Bq = 37 GBq

1 μCi = 37,000 Bq = 37 kBq

1 Bq = 2.7 · 10^-11 Ci = 2.7 · 10^-5 μCi

1 MBq = 0.027 mCi

Calculation of radioactivity

For a mass $m$ (in grams) of an isotope with atomic mass ${displaystyle m_{text{a}}}$ (g/mol) and a half-life ${displaystyle t_{1/2}}$ (s), activity (or radioactivity) is calculated by the expression:

${displaystyle A_{text{Bq}}={frac {m}{m_{text{a}}}}N_{text{A}}{frac {ln 2}{t_{1/2}}}}$

With ${displaystyle N_{text{A}}}$ = 6.02214076 10²³ mol^-1Avogadro's number.

Given that ${displaystyle m/m_{text{a}}}$ is the number of moles ( $n$ ), Activity $A$ is calculated by expression:

${displaystyle A_{text{Bq}}=nN_{text{A}}{frac {ln 2}{t_{1/2}}}}$

For example, on average every gram of potassium contains 0.000117 grams of 40K all other isotopes that occur in nature are stable) that has a ${displaystyle t_{1/2}}$ of 1,277 10⁹ years = 4,030 10¹⁶ s, and has an atomic mass of 39.964 g/mol, so the activity associated with a gram of potassium is 30 Bq.

Calculation of radioactivity of a given mass

The activity in becquereles N medium-life radioactive atoms ${displaystyle t_{1/2}}$ is:

{displaystyle A=-{frac {mathrm {d} N}{mathrm {d} t}}={frac {ln 2}{t_{1/2}}}N}

A mass $m$ of a molar mass isotope $M$ contains ${displaystyle {frac {m}{M}}}$ moles, then ${displaystyle N={frac {m}{M}}N_{mathrm {A} }}$ nuclei, and therefore has an activity:

{displaystyle A={frac {m}{M}}N_{mathrm {A} }{frac {ln 2}{t_{1/2}}}}

with ${displaystyle N_{mathrm {A} }}$ = 6,022 140 76 ×10²³ (constant of Avogadro), $m$ in grams, $M$ in g/mol and ${displaystyle t_{1/2}}$ in seconds.

For example, for a gram of ²²⁶Ra, average life 1600 years (i.e. 1600 × 365 × 24 × 3600 ≈ ${displaystyle 5,05times {10^{10}}{text{ Bq}}}$ ) and atomic mass 226:

{displaystyle A={frac {6,02times {10^{23}}}{226}}{frac {ln 2}{5,05times {10^{10}}}}=3,66times {10^{10}}{text{ Bq}}}

The specific activity of radium 226 is therefore 36.6 GBq/g.

Rounding, we also find the value of the curie, which had been defined as the radioactivity of one gram of radium. The curie is still used in the nuclear industry, as it is a fairly suitable unit for high radioactivity.

If a sample is composed of an element of which only certain isotopes are radioactive, the isotopic composition of the sample must be taken into account. Normally, taking into account its isotopic composition, 1 gram of natural potassium contains 1.17 × 10⁻⁴ grams of ⁴⁰K with a molar mass of 39.963 g/mol (all other isotopes are stable) and a half-life t_1/2 = 1.248 × 10⁹ years or 3.938 × 10 ¹⁶ seconds. Therefore, the activity of one gram of natural potassium is:

{displaystyle A={frac {1,17times {10^{-4}}}{39,963}}N_{mathrm {A} }{frac {ln 2}{t_{1/2}}}=31{text{ Bq}}}

If a material contains different radioactive isotopes, their respective activities are added to give the total activity of the sample considered.

Use to express a quantity of matter

As we have seen, a mass m of a radioactive element has a radioactivity A expressed in «Bq». It usually happens that in the nuclear field the inverse relationship is used: starting from an activity A in «Bq», and knowing the isotopes involved, the amount of a given element can be deduced. By metonymy, it often happens that this quantity of matter is quantified in becquerels.

For example, the amount of cesium-137 dispersed in the environment during the radiological accident in Goiânia in 1987 was estimated at 7 TBq. This isotope has a specific activity of 3,204 TBq/g. The amount of cesium spread is therefore equivalent to about 2.2 g.

This usual metonymy is partly explained by the measurement means involved: the elements are not weighed to obtain their mass, the radioactivity they emit is measured to detect them. Similarly, radon (natural radon, therefore very mainly the 222 isotope) in the atmosphere is measured in Bq per cubic meter of air. The concentration of radon in outdoor air usually varies between 10 and 30 Bq/m³, that is, a mass concentration of 1.7 to 5.2 fg/m³. This order of magnitude (femtogram, fg) is difficult to grasp as mass, which also helps explain the widespread use of Bq and Bq/m³ as a measure of a quantity of radioactive material.

Orders of magnitude of activities

Source Activity

The becquerel (without any other unit) characterizes the activity of a global source:

Human Being: an individual of 70 kg has an activity of 8000 Bq of which 4500 are due to potassium 40.
Source injected during thyroid scan: 40 × 10 ⁶ Bq (about 0.5 MBq per kg of patient weight)..
Source of ⁶⁰Co used for gamma sterilization: from about 15 to more than 1000 kCi (i.e. between ¹⁰ et ¹⁵ Bq).
Activity of a uranium core releasing 1 thermal MW: 3.234 ¹⁶ Bq.
Fuel spent on a nuclear reactor: ¹⁹ Bq.

Specific activity of a substance

The becquerel per gram (or per kilogram) characterizes the total content of radioactive elements:

1 mBq/g (or 1 Bq/L): Limit of liquid discharges considered “non-contaminated” by Electricité de France (high limit to 100 Bq/L for tritium discharges that is very non-diotoxic).
13 mBq/g: Natural seawater radiation: 13 Bq/kg → 13 Bq/L (mainly due to potassium 40)
100 Bq/g: upper limit for very low activity residues according to French regulations.
180 Bq/g to approximately 10 000 Bq/g: Radioactivity of uranium ore, with a concentration of approximately 0.1 to 6% (sometimes more) in uranium 238, in secular balance with its descendants.
12.4 kBq/g: Specific activity of purified uranium 238.
1 MBq/g: Higher limit of “intermediate activity” nuclear waste (AM residues).
2.3 GBq/g: specific plutonium-239 activity.
167 TBq/g: Specific activity of polonium 210.
Over 1 PBq/g: Order of magnitude of the specific activity of short-lived radionuclides in particular those used in the medical field. For example, iodine 131, used in radiation therapy for thyroid conditions, has a specific activity of 4.6 PBq/g, or fluor 18, used for PET images that has a specific activity of 3500 PBq/g. The quantities used are always minimal, usually representing only a few nanograms of the radioisotope considered.

Relationship with other magnitudes related to radiation

Graphic relationships showing between radioactivity and detected ionizing radiation

The following table shows the amounts of radiation in SI and non-SI units. WR (formerly 'Q' factor) is a factor that scales the biological effect for different types of radiation, relative to X-rays. (for example, 1 for beta radiation, 20 for alpha radiation, and a function energy for neutrons) In general, conversion between emission rates, radiation density, fraction absorbed, and biological effects requires knowledge of the geometry between source and target, the energy and type of radiation emitted, between other factors.

Magnitudes related to ionizing radiation Seegradingdiscussgradingedit
Magnitude	Unit	Symbol	Referral	Year	Equivalence SI
Activity (A)	Curriculum	Ci	3.7 × 10¹⁰ s⁻¹	1953	3.7 × 10¹⁰ Bq
	bequerelio	Bq	s⁻¹	1974	Unit SI
	rutherford	Rd	10⁶ s⁻¹	1946	1,000,000 Bq
Exhibition (X)	röntgen	R	esu / 0.001293 g of air	1928	2.58 × 10⁻⁴ C/kg
Absorbed dose (D)	erg		erg⋅g⁻¹	1950	1.0 × 10⁻⁴ Gy
	rad	rad	100 erg⋅g⁻¹	1953	0.010 Gy
	gray	Gy	J⋅kg⁻¹	1974	Unit SI
equivalent dose (H)	rem	rem	100 erg⋅g⁻¹	1971	0.010 Sv
equivalent dose (H)	sievert	Sv	J⋅kg⁻¹ × WR	1977	Unit SI

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