Lecture 20: Radioactivity

recap from last lecture

radioactive decay law

• any radioactive isotope contains a vast number of radioactive nuclei

• they do not all decay at the one time, rather ONE AT A TIME

• this process is RANDOM

• we can predict how many nuclei in a sample will decay over a given time period

• The number of decays ΔN that occur in a very short time interval Δt is then proportional to Δt and to the total number N of radioactive (parent) nuclei present

A given unstable nucleus has a definite probability of decaying in a given time, this probability is called the

• decay constant (same symbol as wavelength)

• characteristic of a particular radionuclide

• radioactive decay is a statistical process

  • the number of nuclei decaying per unit time is proportional to the unit of nuclei present at the time

  • the decay process thus follows an exponential law

radioactive decay law formula

∆N = −λN∆t

• λ = decay constant

• N = number of nuclei present in a sample

• ∆N = decay in a given time interval.

• ∆t = time interval during which decay occurs.

N = N0 e^(−λt)

• N = nuclei remaining

• N0 = original nuclear

Number of disintegration per second

half life formula: time taken for half the radioactive nuclei to decay

Suppose you have 1g of 238U (T1/2 = 4.5×109 y) and 1g of 226Ra (T1/2 =1.6×103 y)

What is the activity of each:

An ancient wooden club is found to contain 290 g of carbon and has an activity of 8.0 decays/s. Determine its age assuming that in living trees the ratio of

14C/12C = 1.3×10-12

T1/2 = 5730 y. (Prob 56/30)

Decay graph for two radioactive samples X and Y are shown

a) Which has a higher probability of decay?

b) What is the half-life of each sample?

a = Y has a higher probability of decay

b = 1h and 3h