Half life?

Question

Can you give me the basic formula on how to find half life

Answer 1

If you're talking about really long half-lives, such as isotopes whose half-lives are thousands of years, you're best off looking it up. For a shorter half-life, you can measure the variable twice and apply a simple equation to determine half-life. This variable might be concentration, radioactivity, capacitor-resistor discharging voltage or anything that follows an exponential decay curve, governed by the the basic decay equation, which is dy/dt = -k*y.
Call the two measurements y0 and y1, made at times t0 and t1. Then the decay equation, if expressed in the base of the natural logarithm e, is
y1 = y0*e^(-(t1-t0)/TC),
where TC is the time constant, i.e., the time required for the measured variable to decrease to 1/e * its starting value. Substitute 2 for e and TC is the half-life. The formula for finding TC from the measurements is
TC = (t1-t0) / (log(y0)-log(y1)) if e-based, and
TC = (t1-t0) / (logbase2(y0)-logbase2(y1)) if 2-based, where logbase2(x) = log(x)/log(2).