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8 Ionizing Radiation and Life
Measures of Radioactivity
Radiation from radioactive materials can be characterized in a variety of ways,
indicated below.
• Activity (A): The activity of a radioactive substance is defined to be the number of
radioactive disintegrations per unit time. One curie (1 Ci) is the activity of 1 gm
of radium, or 3.7 × 10 10 disintegrations per second. A becquerel (Bq) is one
disintegration per second. Since the disintegrations from nuclei to nuclei within
a substance are uncorrelated, dN ∝ Ndt, or
N = N o exp(−t/τ ) .
Activity at any time is then A = (N o /τ ) exp(−t/τ ). The number τ is called
the ‘lifetime’ of the radioactive substance. In a time τ , 1 − 1/e ∼ 63.2%
of the substance has been transformed into daughter products. Alternatively,
N = N o (1/2)
t/t 1/2 , where t 1/2 is called the ‘half-life’ of the substance, since
in each time t 1/2 , half the nuclei initially present have disintegrated. The half-life
is related to the lifetime by t 1/2 = ln e (2) τ = 0.693147 τ .
If a radioactive material is ingested, its lifetime in the body will be determined
not only by its physical lifetime, but also by its metabolic lifetime, i.e. the time
for 1 − 1/e of the substance to be expelled from the body after it is digested and
bound to tissue. The two rates add, so that N = N o (1/2)
t (1/t p +1/t m ) , where t p
is the physical half-life, and t m is the metabolic half-life for the material as if it
were not radioactive.
• Exposure (X): Exposure measures the ionization charge produced by a radioactive substance per unit mass. One ‘röentgen’ (1 R) was originally one electrostatic
unit per cc of dry air at STP. This is equivalent to 2.58 × 10 −4 coulombs per
kilogram.
• Absorbed Dose (D): The Absorbed Dose (also called the Physical Dose) is
defined by the energy deposited by radiation per unit mass. One ‘rad’ is defined
as the deposition of 100 ergs per gram. One ‘gray’ (Gy) is one joule deposited
per kilogram (100 rads).
• Equivalent Dose (H = QD): The Equivalent Dose is the physical dose
multiplied by a “Quality Factor” Q, and is measured in ‘rem’, standing for
‘Radiation-Equivalent-Man’. The factor Q is selected so that QD will have the
same physical radiation damaging effect as the damage caused by X-rays with
the same initial energy, whether the radiation consist of electrons, protons, alpha
particles, or other particles. For example, Q is about 20 for 1 MeV alpha particles,
indicating that 1 MeV alpha particles leaving a physical dose of 1 Gy will produce
the same physical damaging effect as X-rays at 1 MeV whose intensity and
duration leaves a physical dose of 20 Gy, reflecting the fact that α particles are
far more effective in leaving a trail of ions than X-rays at the same energy and
intensity. (See Fig. 8.4).
• Relative Biological Effectiveness: The RBE of a given radiation replaces the
older Quality Factor Q. RBE is defined by the ratio of absorbed dose of the
8 Ionizing Radiation and Life
Measures of Radioactivity
Radiation from radioactive materials can be characterized in a variety of ways,
indicated below.
• Activity (A): The activity of a radioactive substance is defined to be the number of
radioactive disintegrations per unit time. One curie (1 Ci) is the activity of 1 gm
of radium, or 3.7 × 10 10 disintegrations per second. A becquerel (Bq) is one
disintegration per second. Since the disintegrations from nuclei to nuclei within
a substance are uncorrelated, dN ∝ Ndt, or
N = N o exp(−t/τ ) .
Activity at any time is then A = (N o /τ ) exp(−t/τ ). The number τ is called
the ‘lifetime’ of the radioactive substance. In a time τ , 1 − 1/e ∼ 63.2%
of the substance has been transformed into daughter products. Alternatively,
N = N o (1/2)
t/t 1/2 , where t 1/2 is called the ‘half-life’ of the substance, since
in each time t 1/2 , half the nuclei initially present have disintegrated. The half-life
is related to the lifetime by t 1/2 = ln e (2) τ = 0.693147 τ .
If a radioactive material is ingested, its lifetime in the body will be determined
not only by its physical lifetime, but also by its metabolic lifetime, i.e. the time
for 1 − 1/e of the substance to be expelled from the body after it is digested and
bound to tissue. The two rates add, so that N = N o (1/2)
t (1/t p +1/t m ) , where t p
is the physical half-life, and t m is the metabolic half-life for the material as if it
were not radioactive.
• Exposure (X): Exposure measures the ionization charge produced by a radioactive substance per unit mass. One ‘röentgen’ (1 R) was originally one electrostatic
unit per cc of dry air at STP. This is equivalent to 2.58 × 10 −4 coulombs per
kilogram.
• Absorbed Dose (D): The Absorbed Dose (also called the Physical Dose) is
defined by the energy deposited by radiation per unit mass. One ‘rad’ is defined
as the deposition of 100 ergs per gram. One ‘gray’ (Gy) is one joule deposited
per kilogram (100 rads).
• Equivalent Dose (H = QD): The Equivalent Dose is the physical dose
multiplied by a “Quality Factor” Q, and is measured in ‘rem’, standing for
‘Radiation-Equivalent-Man’. The factor Q is selected so that QD will have the
same physical radiation damaging effect as the damage caused by X-rays with
the same initial energy, whether the radiation consist of electrons, protons, alpha
particles, or other particles. For example, Q is about 20 for 1 MeV alpha particles,
indicating that 1 MeV alpha particles leaving a physical dose of 1 Gy will produce
the same physical damaging effect as X-rays at 1 MeV whose intensity and
duration leaves a physical dose of 20 Gy, reflecting the fact that α particles are
far more effective in leaving a trail of ions than X-rays at the same energy and
intensity. (See Fig. 8.4).
• Relative Biological Effectiveness: The RBE of a given radiation replaces the
older Quality Factor Q. RBE is defined by the ratio of absorbed dose of the