Half Life It is impossible to predict when an individual atom will decay. Review of Half life If living creatures had half lives the way radioactive atoms do, the world would be a very different place. Suppose there's an alien species with a half life of 70 years. You randomly pick out 16 baby aliens and track them to see how long they live. After 70 years 8 of them will still be alive.

If you tracked a group of human babies, you might get the same results. Remember that the halflife is always the same, regardless of how old the aliens are. After another 70 years, 4 of those 8 will still be living, now 140 years old. And half of those--2 aliens--will survive to the age of 210. Another 70 years go by, and there's one alien left, age 280.

If the study is continued after 280 years with the only remaining alien and a new batch of 15 babies. Now there are 16 aliens in the study again, and, as before, 8 of them will be alive after 70 years. Why should our old boy survive??? He has just as much chance of surviving the next 70 years as any one of the 15 babies. In fact, he has just as good a chance as any one of them of living another 280 years. The probability of decay has nothing to do with the history of any individual atom, or alien; otherwise the halflife wouldn't be constant. Radioactive atoms just don't grow old the way we do!

Half life can also be modelled using the flow of water from a burette. This needs to be very slow flowing to ensure the correct results. You should think about why the flow rate is decreasing! Record the volume remaining as time progresses Fluid pressure is dependant on the height of the column of liquid. Therefore if the height halves so does the pressure and the rate of flow This means the fluid level will drop half as much in the same time This will therefore produce an exponential style decay curve!

The second way of modelling the decay is to use the dice, throw them and take out all the sixes. Count the number remaining and plot a graph of the number remaining against the number of throws. Exchange results with everyone else to improve the accuracy of your experiment.

Radioactive Half-Life For a particular decay process, it will always take the same amount of time for the number of nuclei to halve. It could be from 100 nuclei to 50 or from 10 6 to 5x10 5. The half life is the average time taken for half the nuclei to decay The half life is the average time taken for half the nuclei to decay y3.html htm

A In radioactive decay we know that if we have twice as many atoms, the rate of decay (A) will double. ACTIVITY This is sometimes known as the ACTIVITY of the substance. ie The constant of proportionality is called the decay constant what are its units?…... s -1 The decay constant represents the proportion of the atoms that decay in 1s. It is fixed for any particular nuclear decay. If it is large the decay is rapid If it is large the decay is rapid. A  N A = N

t 1/2 = The link between the decay constant and the half life is…… N, The rate of decay changes because the number of undecayed atoms, N, changes!!!!Remember that the number of atoms involved is likely to be in the millions! ACTIVITYbequerel (Bq). The ACTIVITY is measured in bequerel (Bq). 1 Bq = 1 decay per second. A = N

You have just seen e e is a pure number = N N is the number of particles left after time t N o N o is the original number of particles. A = N exponential law of radioactive decay This is the exponential law of radioactive decay. This first order differential equation can be integrated to show that It is truly written as the rate of change of the number of atoms instead of activity. The minus sign shows the decrease in number! N = N o e - t dN/dt = - N

There is no known way of changing the half-life of a nuclide. eg. The half life of a substance is 2 years. How much will be left after 8 years? soln. 8 years = 4 half-lives so the number of particles left will be 1/2 x 1/2 x 1/2 x1/2 = 1/16th Note that if you do not have a whole number of half-lives, you must use the previous equation

When one half life has passed, t = t 1/2 and N = N 0 /2 so the equation becomes ie Taking natural logarithms of both sides we obtain: ln (1/2) = - t 1/2 and so t 1/2 = ln(2) / t 1/2 = Therefore the link between the decay constant and the half life is…… This is the bit we need to know again!

EXAMPLE Uranium 238 has a half life of 4.51 x 10 9 years. Calculate the number of particles of uranium 238 that will exist after x 10 9 years from a sample of 1 kg. (N A = 6.02x10 23 mol -1 ) Solution: We need the half life in seconds T 1/2 = 4.51x10 9 x x 24 x 60x60 = x s Notice that it is not a whole number of half lives so we have to use BUT we don’t know - examiners frequently do this! Fortunately we know that t 1/2 = / so = / t 1/2 = / x s = x s -1 t = 2.255x10 9 years = 2.225x10 9 x x 24 x 3600 t = 7.1 x s so == = = 0.707

ie 70.7% is left BUT how many were there to start with? so == = = mole is 238g  238g is N A  kg is N A  1kg is N A / = 6.02x10 23 / = 2.53 x particles Number Left = x 2.53 x = 1.79 x Particles