Environmental Engineering FOURTH EDITION

Radioactive Waste 315

Table 16-1. Some Important Radionuclides

Radionuclide Type of radiation Half-life

Krypton-85

Strontium-90

Iodine- 1 3 1

Cesium-137

Tritium (Hydrogen-3)

Carbon-14

Uranium-235

Uranium-238

Plutonium-23 9

C 0 b al t -60

Beta and gamma

Beta

Beta and gamma

Beta and gamma

Beta

Beta and gamma

Beta

Alpha

Alpha

Alpha

10 years

29 years

8.3 days

30 years

12 years

5 years

5770 years

7.1 x lo8 years

4.9 x io9 years

24,600 years

That is, one-half of the radioactive atoms have decayed (or disintegrated) during each

time period ~112. This time period t1/2 is called the radiological half-life, or sometimes

simply the half-life. Looking at Fig. 16-1, we see that at t = 2t1/2, N becomes &No; at

t = 3t1/2, N becomes $fvo; and so on. Equation (16.2) is so constructed that N never

becomes zero in any fimte time period; for every half-life that passes, the number of

atoms is halved. If the decay constant Kb is known, the half-life may be determined

from Q. (16.2):

ln2 = Kbt1/2. (16.3)

The radiological half-lives of selected radionuclides are presented in Table 16-1.

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EXAMPLE 16.1. An amount of 10.0 g of pure 6C" is prepared. The equation for this

nuclear reaction is

6C'l + leo + sB1'.

The half-life of C-11 is 21 min. How many grams of C-11 will be left 24 h after the

preparation? (Note that one atomic mass unit (amu) = 1.66 x

Equation (16.2) refers to the number of atoms, so we must calculate the number

of atoms in 1 .O g of carbon-1 1

1 g = (A mole) (6.02 x 1023 atoms/mole ) = 5.47 x 1022 atoms = NO.

g.)

Applying Eq. (16.2),

24h = (24)(60) = 1440min = t

Kb = h 2/t1/2 = 0.693/21 = 0.033 min-'