Mr. Shields Regents Chemistry U02 L03

Nuclear Decay Series

Uranium has an atomic number greater than83. Therefore it is naturally radioactive.

Most abundant isotope

Alpha Particle

Thorium DecayOf course Thorium’s atomic number is alsogreater than 83. So it to is Radioactive andGoes through beta decay.

234Pa + 0e91 -1

Protactinium

U-238 Decay Series

Protactinium decaysNext and so on untilwe reach a stable Non-radioactive Isotope of lead

Pb-206 Atomic No. 82

U-238 Decay Series

Decay Series

U-238 IS NOT the only radioactive isotope thatHas a specific decay series.

All radioisotopes have specific decay paths they follow to ultimately reach stability

Decay Series Time Span

The next Question you might consider askingis how long does this decay process take?

The half life of U-238 is about 4.5 billionyears which is around the age of theearth so only about half of the uraniumInitially present when the earth formed has Decayed to date.

Which leads us into a discussion of Nuclear Half life

Nuclear Half-life

Unstable nuclei emit either an alpha, beta or positron particles to try to shed mass or improve their N/P ratio.

But can we predict when a nucleus willDisintegrate?

The answer is NO for individual nuclei

But YES if we look at large #’s of atoms.

Nuclear Half-life

Every statistically large group of radioactivenuclei decays at a predictable rate.

This is called the half-life of the nuclide

Half life is the time it takes for half (50%) of theRadioactive nuclei to decay to the daughterNuclide

Nuclear Half-life

The Half life of any nuclide is independent of:

Temperature, Pressureor

Amount of material left

Beanium decay

64 beans

32 beans

16 beans

8 beans4 beans

Successive half cycles

1

2

34

50%

What does the graph of radioactive decay look like?

This is an EXPONENTIALDECAY CURVE

Loss of mass due to Decay

Amount of beanium 64 32 16 8 4Fraction left 1 ½ ¼ 1/8 1/16Half life’s 1 2 3 4

If each half life took 2 minutes then 4half lives would take 8 min.

The equation for the No. of half livesis equal to:

T (elapsed) / T (half Life)32 minutes / 4 minutes = 8 half life’s

Carbon 14 is a radionuclide used to date Once living archeological finds

Carbon–14 Half-life = 5730 years

22,920/5730 = 4 Half-life’s

t0

Half-Lives In order to solve these half problems a table like the one below is useful. For instance, If we have 40 grams of an original sample of Ra-226 how much is left after 8100 years?

½ life period % original remaining

Time Elapsed

Amount left

0 100 0 40 grams1 50 1620 yrs 20 grams2 25 3240 ?3 12.5 4860 ?4 6.25 6480 ?5 3.125 8100 ?

10 grams

5 grams

2.5 grams

1.25 grams

Problem:

A sample of Iodine-131 had an original

mass of 16g. How much will remain in 24

days if the half life is 8 days?

Step 1: Half life’s = T (elapsed) / T half life = 24/8 = 3 Step 2: 16g (starting amount) 8 4 2gHalf lives 1 2 3

Problem: What is the original amount of a sample of H–

3 if after 36.8years 2.0g are left ?

Table N tells us that the half life of H-3 is 12.26 yrs.

36.8 yrs / 12.26 yrs = 3 half lives.

Now lets work backward

Half life 3 2 gramsHalf life 2 4 gramsHalf life 1 8 gramsTime zero 16 grams

Problem: How many ½ life periods have passed if a

sample has decayed to 1/16 of its original amount?

Time zero 1x original amountFirst half life ½ original amountSecond half life ¼ original amountThird half life 1/8Fourth half life 1/16

Problem:

What is the ½ life of a sample if after 40 years 25 grams of an original 400 gram sample is left ?

Step 1:25 grams 4 half lifes50 3 half lifes100 g 2 half lifes200 g 1 half life400 g time zero

Step 2:

Elapsed time = # HLHalf-life

40 years = 4 HLHalf-life

Half life = 10 years