Radiation Dosimetry

Units of Radioactivity

As was written, radioactivity (activity of certain radionuclides) is the process by which an unstable nucleus spontaneosly and randomly disintegrates to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic partices or high energy rays. This decay occurs at a constant, predictable rate that is referred to as decay constant. As a result, a measure of radioactivity is based on counting of disintegrations per second. The activity depends only on the number of decays per second, not on the type of decay, the energy of the decay products, or the biological effects of the radiation. It can be used to characterize the rate of emission of ionizing radiation.

Units of radioactivity (the curie and the becquerel) can be also used to characterize an overall quantity of controlled or accidental releases of radioactive atoms. Because the probability of decay is a fixed physical quantity, for a known number of atoms of a particular radionuclide, a predictable number will decay in a given time. For example, according to the Nuclear Safety Commission (NSC) of Japan, the total amounts of activity released during Fukushima Daiichi accident between 11 March and 5 April were about 130 PBq (petabecquerels, 3.5 megacuries) for iodine-131 and 11 PBq for caesium-137.

According to the UNSCEAR, from 1998 to 2002, the global annual average releases of tritium to the atmosphere and to the aqueous environment from nuclear facilities were estimated to be 11.7 PBq and 16.0 PBq, respectively. Note that, tritium emits low-energy beta particles with a short range in body tissues and, therefore, poses a risk to health as a result of internal exposure only following ingestion in drinking water or food, or inhalation or absorption through the skin. According to the ICRP, a biological half-time of tritium is 10 days for HTO and 40 days for OBT (organically bound tritium) formed from HTO in the body of adults.

See also: SOURCES, EFFECTS AND RISKS OF IONIZING RADIATION, UNSCEAR 2016, ISBN: 978-92-1-142316-7.

Historically, the original unit for measuring the amount of radioactivity was the curie (symbol Ci), which is a non-SI unit of radioactivity defined in 1910.  The SI unit for measuring the amount of radioactivity is the becquerel (symbol Bq). The becquerel is named in honour of Henri Becquerel.  Rutherford (symbol Rd) is also a non-SI unit defined as the activity of a quantity of radioactive material in which one million nuclei decay per second. This unit was introduced in 1946, but after the becquerel was introduced in 1975, the rutherford became obsolete.

Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Radiation Protection

The original unit for measuring the amount of radioactivity was the curie (symbol Ci), which is a non-SI unit of radioactivity defined in 1910. A curie was originally named in honour of Pierre Curie, but was considered at least by some to be in honour of Marie Curie as well. A curie was originally defined as equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. Currently, a curie is defined as 1Ci = 3.7 x 10¹⁰ disintegrations per second. Therefore:

1Ci = 3.7 x 10¹⁰ Bq = 37 GBq

One curie is a large amount of activity. The typical human body contains roughly 0.1 μCi (14 mg) of naturally occurring potassium-40. As well, a human body containing 16 kg of carbon would also have about 0.1 μCi of carbon-14 (24 nanograms). Activities measured in a nuclear power plant (except irradiated fuel) often have usually lower activity than curie, and the following multiples are often used:

1 mCi (milicurie) = 1E-3 Ci

1 µCi (microcurie) = 1E-6 Ci

While its continued use is discouraged by many institutions, the curie is still widely used throughout the government, industry and medicine in the world.

Curie – Examples

The relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown in the figure. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

The following figure illustrates the amount of material necessary for 1 curie of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 1 curie of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Units of Radioactivity

The SI unit for measuring the amount of radioactivity is the becquerel (symbol Bq). The becquerel is named in honour of Henri Becquerel, a French physicist who discovered radioactivity in 1896. One becquerel (1Bq) is equal to 1 disintegration per second.

An older unit of radioactivity is the curie. The curie was originally defined as equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. Currently, a curie is defined using becquerels as 1Ci = 3.7 x 10¹⁰ disintegrations per second. Therefore

1Ci = 3.7 x 10¹⁰ Bq = 37 GBq

One becquerel is very small amount of activity. The typical human body contains roughly 3.7 kBq (14 mg) of naturally occurring potassium-40. As well, a human body containing 16 kg of carbon would also have about 3.7 kBq of carbon-14 (24 nanograms). Activities measured in a nuclear power plant (except irradiated fuel) often have usually higher activity than becquerel, and the following multiples are often used:

1 kBq (kilobecquerel) = 1E3 Bq

1 MBq (megabecquerel) = 1E6 Bq

1 GBq (gigabecquerel) = 1E9 Bq

1 TBq (terabecquerel) = 1E12 Bq

Becquerel – Examples

The relationship between half-life and the amount of a radionuclide required to give an activity of 37 GBq (1 Ci) is shown in the figure. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

The following figure illustrates the amount of material necessary for 37 GBq of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 37 GBq of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

 

Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Units of Radioactivity

The original unit for measuring the amount of radioactivity was the curie (symbol Ci), which is a non-SI unit of radioactivity defined in 1910. Rutherford (symbol Rd) is also a non-SI unit defined as the activity of a quantity of radioactive material in which one million nuclei decay per second. This unit was introduced in 1946, but after the becquerel was introduced in 1975, the rutherford became obsolete.

Currently, one rutherford is equivalent to one megabecquerel:

1Rd = 1 x 10⁶ Bq = 1 MBq

One rutherford is quite large amount of activity. The typical human body contains roughly 0.0037 Rd (14 mg) of naturally occurring potassium-40. As well, a human body containing 16 kg of carbon would also have about 0.0037 Rd of carbon-14 (24 nanograms).

Rutherford – Examples

The relationship between half-life and the amount of a radionuclide required to give an activity of one rutherford is shown in the figure. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

The following figure illustrates the amount of material necessary for 37 kilorutherford of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 37 kRd of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Units of Radioactivity

Historically, the original unit for measuring the amount of radioactivity was the curie (symbol Ci), which is a non-SI unit of radioactivity defined in 1910.  The SI unit for measuring the amount of radioactivity is the becquerel (symbol Bq). The becquerel is named in honour of Henri Becquerel.  Rutherford (symbol Rd) is also a non-SI unit defined as the activity of a quantity of radioactive material in which one million nuclei decay per second. This unit was introduced in 1946, but after the becquerel was introduced in 1975, the rutherford became obsolete.

Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Radiation Protection

Curie to Becquerel – Conversion

The original unit for measuring the amount of radioactivity was the curie (symbol Ci), which is a non-SI unit of radioactivity defined in 1910. A curie was originally named in honour of Pierre Curie, but was considered at least by some to be in honour of Marie Curie as well. A curie was originally defined as equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. Currently, a curie is defined as 1Ci = 3.7 x 10¹⁰ disintegrations per second. Therefore:

1Ci = 3.7 x 10¹⁰ Bq = 37 GBq

The SI unit for measuring the amount of radioactivity is the becquerel (symbol Bq). The becquerel is named in honour of Henri Becquerel, a French physicist who discovered radioactivity in 1896. One becquerel (1Bq) is equal to 1 disintegration per second.

Curie to Becquerel – Problem with Solution

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

See also:

Units of Radioactivity

The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. The radioactive decay of certain number of atoms (mass) is exponential in time.

Radioactive decay law: N = N.e^-λt

The rate of nuclear decay is also measured in terms of half-lives. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. In 14 more days, half of that remaining half will decay, and so on. Half lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive (at the time of production) but will obviously lose its radioactivity rapidly. No matter how long or short the half life is, after seven half lives have passed, there is less than 1 percent of the initial activity remaining.

The radioactive decay law can be derived also for activity calculations or mass of radioactive material calculations:

(Number of nuclei) N = N.e^-λt     (Activity) A = A.e^-λt      (Mass) m = m.e^-λt

, where N (number of particles) is the total number of particles in the sample, A (total activity) is the number of decays per unit time of a radioactive sample, m is the mass of remaining radioactive material.

Decay Constant and Half-Life

In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. There is a relation between the half-life (t_1/2) and the decay constant λ. The relationship can be derived from decay law by setting N = ½ N_o. This gives:

where ln 2 (the natural log of 2) equals 0.693. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa.

Decay Constant and Radioactivity

The relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown in the figure. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

The following figure illustrates the amount of material necessary for 1 curie of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 1 curie of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

Example – Calculation of Radioactivity

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

1. The number of iodine-131 atoms initially present.
2. The activity of the iodine-131 in curies.
3. The number of iodine-131 atoms that will remain in 50 days.
4. The time it will take for the activity to reach 0.1 mCi.

Solution:

1. The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131 = (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

2. The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

 

See also:

Decay Law

Photoelectric Effect

 

• The photoelectric effect dominates at low-energies of gamma rays.
• The photoelectric effect leads to the emission of photoelectrons from matter when light (photons) shines upon them.
• The maximum energy an electron can receive in any one interaction is hν.
• Electrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy.
• A free electron (e.g. from atomic cloud) cannot absorb entire energy of the incident photon. This is a result of the need to conserve both momentum and energy.
• The cross-section for the emission of n=1 (K-shell) photoelectrons is higher than that of n=2 (L-shell) photoelectrons. This is a result of the need to conserve momentum and energy.

Definition of Photoelectric effect

In the photoelectric effect, a photon undergoes an interaction with an electron which is bound in an atom. In this interaction the incident photon completely disappears and an energetic photoelectron is ejected by the atom from one of its bound shells. The kinetic energy of the ejected photoelectron (E_e) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (E_b).

E_e=hν-E_b

Therefore photoelectrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy – the binding energy of the electron – the work function of the material. For gamma rays with energies of more than hundreds keV, the photoelectron carries off the majority of the incident photon energy – hν.Following a photoelectric interaction, an ionized absorber atom is created with a vacancy in one of its bound shells. This vacancy is will be quickly filled by an electron from a shell with a lower binding energy (other shells) or through capture of a free electron from the material. The rearrangement of electrons from other shells creates another vacancy, which, in turn, is filled by an electron from an even lower binding energy shell. Therefore a cascade of more characteristic X-rays can be also generated. The probability of characteristic x-ray emission decreases as the atomic number of the absorber decreases. Sometimes , the emission of an Auger electron occurs.

Cross-Sections of Photoelectric Effect

At small values of gamma ray energy the photoelectric effect dominates. The mechanism is also enhaced for materials of high atomic number Z. It is not simple to derive analytic expression for the probability of photoelectric absorption of gamma ray per atom over all ranges of gamma ray energies. The probability of photoelectric absorption per unit mass is approximately proportional to:

τ_{(photoelectric)} = constant x Z^N/E^3.5

where Z is the atomic number, the exponent n varies between 4 and 5. E is the energy of the incident photon. The proportionality to higher powers of the atomic number Z is the main reason for using of high Z materials, such as lead or depleted uranium in gamma ray shields.Although the probability of the photoelectric absorption of gamma photon decreases, in general, with increasing photon energy, there are sharp discontinuities in the cross-section curve. These are called “absoption edges” and they correspond to the binding energies of electrons from atom’s bound shells. For photons with the energy just above the edge, the photon energy is just sufficient to undergo the photoelectric interaction with electron from  bound shell, let say K-shell. The probability of such interaction is just above this edge much greater than that of photons of energy slightly below this edge. For gamma photons below this edge the interaction with electron from K-shell in energetically impossible and therefore the probability drops abruptly. These edges occur also at binding energies of electrons from other shells (L, M, N …..).

Cross section of photoelectric effect.

See also:

Characteristics of Gamma Rays

See also:

Interaction of Gamma Radiation with Matter

See also:

Compton Scattering

Positron-Electron Pair Production

In general, pair production is a phenomenon of nature where energy is direct converted to matter. The phenomenon of pair production can be view two different ways. One way is as a particle and antiparticle and the other is as a particle and a hole. The first way can be represented by formation of electron and positron, from a packet of electromagnetic energy (high energy photon – gamma ray) traveling through matter.  It is one of the possible ways in which gamma rays interact with matter. At high energies this interaction dominates. In order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy.If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles.The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.Moreover, the positron is the anti-particle of the electron, so when a positron comes to rest, it interacts with another electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass back to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons). The pair production phenomenon is therefore connected with creation and destruction of matter in one reaction.

Positron-Electron Pair Production – Cross-Section

The probability of pair production, characterized by cross section, is a very complicated function based on quantum mechanics. In general the cross section increases approximately with the square of atomic number (σ_p ~ Z²) and increases with photon energy, but this dependence is much more complex.

Cross section of pair production  in nuclear field and electron field.

See also:

Compton Scattering

See also:

Interaction of Gamma Radiation with Matter

See also:

Attenuation