Unit: Nuclear Chemistry

Half-Life

Day 2 –

Notes

After today you will be able to…

• Identify the factor that nuclear stability is dependent on.• Calculate the half-life for a

given radioisotope.• Calculate how much of a

radioisotope remains after a given amount of time.

Nuclear Stability• Close to 2,000 different nuclei are

known.• Approximately 260 are stable and

do not decay or change with time.• The stability (resistance to

change) depends on its neutron:proton ratio.

Nuclear Stability• Plotting a graph

of number of neutrons vs. number of protons for each element results in a region called the band of stability.

Nuclear Stability• For elements

with low atomic numbers (below 20) the ratio of neutrons:protons is about 1.–Example:

(6n/6p = 1)C12

6

Nuclear Stability• For elements with

higher atomic numbers, stable nuclei have more neutrons than protons. The ratio of n:p is closer to 1.5 for these heavier elements.– Example:

124n/82p = approx. 1.5

Pb20682

Nuclear Stability• The neutron:proton ratio is important because it determines the type of decay that occurs.• All nuclei that have an atomic number greater than 83 are radioactive.

Ever wonder why some atomic masses listed on the Periodic Table have ( ) around them? Because their

atomic masses are estimated due to

radioactive decay!

Half-LifeHalf-life: (t1/2) the time required for half of the nuclei of a radioisotope sample to decay to products.• Example: If you have 20 atoms of Radon-

222, the half life is ~4 days. How many atoms remain at the end of two half lives?

0 t1/2 1 t1/2 2 t1/2

4 days 8 days

20 atoms initially

10 atoms 5 atoms remain

Half-Life• We can

represent half-life graphically as well.—Example:

Carbon-14

However, very seldom do we count atoms.

Therefore it is more appropriate to calculate amount that remains in

terms of mass.

Half-Life• Example: Carbon-14 emits beta radiation

and decays with a half-life (t1/2) of 5730 years. Assume you start with a mass of 2.00x10-12g of carbon-14.

a.How long is three half-lives?b.How many grams of the isotope

remain at the end of three half-lives?c. 3(5730) =

d. 2.00x10-12g x 1/2 x 1/2 x 1/2 =

17,190 years

2.5x10-13g

Half-Lifeb. How many grams of the isotope remain at

the end of three half-lives?

Alternatively, part b can also be calculated like this:0 t1/2

2.00x10-

12g initially

1.00x10-

12g2.50x10-

13g remains

1 t1/2 2 t1/2 3 t1/2

5.00x10-

13g

x 1/2 x 1/2 x 1/2

Half-Life• Example: Manganese-56 is a beta emitter

with a half-life of 2.6 hours. a. How many half-lives did the sample go

through at the end of 10.4 hours? b. What is the mass of maganese-56 in a

1.0mg sample of the isotope at the end of 10.4 hours?c. 10.4 h/2.6 h =d. 1.0mg x 1/2 x 1/2 x 1/2 x 1/2 =

4 half-lives 0.063

mg

Questions?Complete and turn

in the exit ticket.