21 · NUCLEAR AND RADIOCHEMISTRYof the radionuclide have disintegrated. The factor kis related to the half-life of the
decay by the equationt (^1) ⁄ 2
0.693
k
(see page 258). If kis required in the units of s^1 ,t (^1) ⁄ 2 must be in the units of
seconds.
Key points about half-life
●A long half-live indicates that it will be a long time before the radioactivity of a
sample containing atoms of that nuclide fades to a near-zero level. Such a radio-
nuclide is said to be long-lived. Similarly, a radionuclide with a short half-life is
said to be short-lived. Most of the world is slowly becoming less radioactive, as the
radioactive elements brought together when the earth was formed (about 4.5
billion years ago) decay away.
●Short-lived radionuclides emit nuclear radiation more rapidly than long-lived
radionuclides, and a sample of a short-lived radionuclide will (statistically)
undergo more disintegrations per second than the same number of nuclei of a sta-
ble radionuclide. It follows that short-lived radionuclides give out more intense
nuclear radiation than long-lived radionuclides, but for a shorter time.
●The disintegration of radionuclides is random. Think of 100 radium-226 atoms
decaying with a half-life of 1600 years. Although it is statistically likely that 50 Ra
atoms will have disintegrated after 1600 years, we cannot predict whichindividual
Ra atoms willdisintegrate during this time.
Plot of radionuclide mass against time
Figure 21.3 shows the fall in mass of samples of three radionuclides (with an initial
mass of 1 g each) over 5 days, calculated using the equation mtm 0 ekt.
●All three curves are drawn on the same scale. The longest lived radionuclide
(^13755 Cs) has undergone a negligible amount of decay over 5 days.
404
1.0
0.5
Mass of isotope that remains/g^0
1 3 4 5
Time/days
0 2
(c)
(b)
(a)
Fig. 21.3The decay of 1 g of each of three radionuclides: curve
(a) 1124 Na(t (^1) / 2 15.0 h); curve (b)^13153 I (t (^1) / 2 8.04 days); curve
(c)^13755 Cs (t (^1) / 2 30.17 yr).
Half-life 1
Sketch a graph showing
the decay of 1 g of
uranium-238 on the same
time scale as shown in
Fig. 21.3.
Exercise 21E