Characteristic decay scheme

The modes and characteristic energies that comprise the decay scheme for each radioisotope are specific. If instrumentation is sufficiently sensitive, it is possible to identify which isotopes are present in a sample, or alternatively, to measure only the radioisotope of interest within a sample containing several radioisotopes.

Half‐life (T_1⁄2)

Probably the best known property of radioactivity is the half‐life T_1⁄2. After one‐ half life has elapsed, the number of radioactive decay events in a sample per unit time will be observed to have reduced by one‐half. The decay rate or activity at any time t can be described mathematically:

At = A0 e‐^.693 t/T1⁄2

e^-.693 is equal to 1⁄2, and the exponent t/ T_1⁄2 describes the number of elapsed half‐lives. Therefore, t and T_1⁄2 must be expressed in the same unit. For example, the half‐life of I‐131 is 8.0 days. If a vial were labeled “29 mCi at 1pm June 3,” the activity in the vial at 1am June 6 is:

29 mCi e‐.693 ^(2.5/8.0) =23 mCi

Alternatively, if n is the number of elapsed half‐lives, then:

A_t = A_0 (1/2)ⁿ

29 mCi (1/2) ^0.31 = 23 mCi

Half‐lives range from billionths of a second to billions of years. The half‐life is characteristic of the radioisotope, and cannot be inferred. The half‐life is included with the description of the decay scheme.

Decay constant (λ)

The number of decay events in a sample per unit time, or activity A, is proportional to the number of radioactive parent atoms N in the sample; A = ‐λ N. For example, the decay constant for 99mTc is 0.115/hour. The half‐life is related to the isotope’s decay constant; λ = .693 / T_1/2. Thus, we can also write the decay equation:

A_t = A₀ e‐^λt

For example, if a vial contains 100 mCi of Tc‐99m at 7 am, the activity at 7 pm is:

100 mCi e^{‐0.115/hr x 12 hr} = 25 mCi

When using any of these equations, be sure that the same unit of time, whether hours or years, is used to measure both half life T_1/2, or decay constant, and elapsed time t.

Measures of activity (A)

The number of disintegrations, or decay events, or nuclear transformations, in a sample per unit time is its activity A. Two common informal units are disintegrations per second and disintegrations per minute.

Curie (Ci)

The US unit of activity is the curie (Ci). One curie is 2.2×10¹² disintegrations per minute, or 3.7×10¹⁰disintegrations per second. Common multiples are the millicurie and microcurie.

Becquerel (Bq)

The SI unit of activity is the becquerel (Bq). One becquerel is 1 disintegration per second. The common multiple is the megabecquerel. Note that 1 mCi = 37 MBq.