easy 10 pts What does the halflife of a radioactive source r

easy 10 pts

What does the half-life of a radioactive source represent? If Cobalt-60 were calibrated to have an initial decay-rate of R_0 = 15 muCi (micro-Curies) about 15 years ago, what would be the approximate strength of the source now? Show the calculations that you performed in order to come to your conclusions

Solution

a)Half-life (t₁₂) is the time required for the amount of something to fall to half its initial value. The term is very commonly used in nuclear physics to describe how quickly unstable atoms undergo decay, or how long stable atoms survive, radioactive decay, and it is also used more generally of any type of exponential or non-exponential decay

b) R(t) =R(0) e^-(lambda t)

You first need to evaluate lambda. You can do this from the half life value given since at half life R/R0 =1/2
1/2 =e^-(lambda t)
ln (1/2) = -lambda x t
Therefore, lambda = -1/t ln(0.5)
Where t is your 5.3 years.

lambda = -1/5.3 x (-0.6931)
lambda = 0.1307

Then once you have a value for lambda you evaluate
R = 15 e^-(0.1307 x 15) (uC)
Where t this time is 15 Years.
R =15e^-(1.9605)
R = 15 x 0.140788
R = 2.11 uC

The strength of the source after 15 years is 2.1 uC