Half-Life 7.2

A large unstable isotope will decay many times until it becomes a stable daughter isotope. If we take all the decays that the parent isotope undergoes, we get a decay series.

Radioactive decay occurs at a certain speed, or rate, for each kind of radioactive isotope. as a sample decays, the amount of radioactive isotopes that remain become less and less radioactive isotopes decay at a _________________ rate constant

100% 50% 25% 12.5% 0% 50% 75% 87.5% 1 50% 50%/yr half-life 1 year → 2 year → 3 year → 4 year P P P P P P P P P P D D D D D D D D D D P P P P P D D D D D P P D D D D D D D P: ______ D: ______ What is the rate of radioactive decay? Every _____ year(s), ________ of the parent isotope decays → ___________ This is called a ______________ 100% 50% 25% 12.5% 0% 50% 75% 87.5% 1 50% 50%/yr half-life

half Half-life: the amount of time it takes for _________ of the nuclei in a sample of radioactive isotope to decay. Each half-life means that ________ of the radioactive isotope has decayed. 50% 100% 50% 25% 12.5% 6.25%

After 2 half lives, 25% of U-235 remains 100% 1/1 50% 1/2 25% 1/4 12.5% 1/8 6.25% 1/16 6.25% or 1/16 1420/710 = 2 half lives After 2 half lives, 25% of U-235 remains

2.6 3.9 5.2 5 6 21/7 = 3 (5)(7) = 35 90/45 = 2 (4)(45) = 180 s

To find the amount of parent isotope remaining after x half-lives, multiply the original amount by the % remaining. 100% 50% 100 x ½ = 50 g 58 25% 100 x ½ x ½ = 25 g 87 12.5% 100 x ½ x ½ x ½ = 12.5 g 116 6.25% 100 x ½ x ½ x ½ x ½ = 6.25 g

1 50% 32 g 2 25% 16 g 116 6.25% 4 g

1 half-life so 128(0.50) = 64 g 2 half-lives so 128(0.50)(0.50) = 32 g 128(0.50)(0.50)(0.5) = 16 g

What is the half-life of the class? _____________ How many people are remaining after 2 half-lives? _____________

2.5 years 6 years 8.6 years 12.5% 20/2.5 = 8 half-lives

100% 0% 1:0 1 50% 50% 1:1 2 25% 75% 1:3 3 12.5% 87.5% 1:7 4 6.25% 93.75 1:15

P:D = 1:7 means 3 half-lives 3 x 7 years = 21 years old P = 100 g – 75 g = 25 g P:D = 25 : 75 = 1 : 3 = 2 half-lives 2 x 7 years = 14 years have passed

Carbon-14 5730 dies

25 g 50 g (25/200)(100)=12.5% 25% 3 2 (3)(5730)=17190 yrs 11460 yrs