either the rate
constant or the
half-life is known, the other can be calculated. Half-lives usually
are used because they have an immediate physical meaning.
The exponential decay curve (fig 4
opposite) can be used to give the rate
law a physical meaning. The rate of change of concentration
with time, d[C-14]/dt, is simply the slope
of the first-order
decay curve at any time, t.
Because carbon-14 is disappearing, the
slope is negative. By drawing a tangent line to the decay curve
at several points and examining the slope, you should be able to
verify that the slope of the curve at any time t is proportional
to the remaining concentration of carbon-14, measured in the vertical
direction. This is what the rate law for a first-order process means: