Wednesday, November 4th, 2015

The blue grid below represents a quantity of C14. Each time you click,one half-life goes by and turns red. C14 – blue N14 - red

As we begin notice that no time has gone by and that 100% of the material is C14

Half

lives

% C14 %N14 Ratio of

C14 to N14

0 100% 0% no ratio

2

The grid below represents a quantity of C14. Each time you click,one half-life goes by and you see red. C14 – blue N14 - red

Half

lives

% C14 %N14 Ratio of

C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

After 1 half-life (5730 years), 50% ofthe C14 has decayed into N14. The ratioof C14 to N14 is 1:1. There are equalamounts of the 2 elements. 3

The blue grid below represents a quantity of C14. Each time you click,one half-life goes by and you see red .C14 – blue N14 - red

Half

lives

% C14 %N14 Ratio of

C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

2 25% 75% 1:3

Now 2 half-lives have gone by for a totalof 11,460 years. Half of the C14 that waspresent at the end of half-life #1 has nowdecayed to N14. Notice the C:N ratio. Itwill be useful later.

4

The blue grid below represents a quantity of C14. Each time you click,one half-life goes by and you see red. C14 – blue N14 - red

Half

lives

% C14 %N14 Ratio of

C14 to N14

0 100% 0% no ratio

1 50% 50% 1:1

2 25% 75% 1:3

3 12.5% 87.5% 1:7

After 3 half-lives (17,190 years) only12.5% of the original C14 remains. Foreach half-life period half of the materialpresent decays. And again, notice the ratio, 1:7

5

6

What is the half life represented in this graph?

7

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

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 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 4 half lives would take 8 min.

The equation for the No. of half lives is equal to:

T (elapsed – total) / T (one half Life)

32 minutes / 4 minutes = 8 half life’s

• 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 1:

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: How many half lives? Half life= T (elapsed) / T half life = 24/8 = 3 

Step 2: 16g (starting amount) 8 4 2g

Problem 2:• What is the original amount of a sample of H–3 if after

36.8 years 2.0g are left if the half life of H-3 is 12.26 years?

36.8 yrs / 12.26 yrs = 3 half lives.

___ ___ ___ 2 g Work backwards!

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

Problem 3:

• How many half 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 4:

•What is the ½ life of a sample if after 40 years 25 grams of an original 400 gram sample is left ? Step 1:

400 200 100 50 254 half lives

Step 2:

Elapsed time = # HL 40 years = 4 HLHalf-life Half-life

Half life = 10 years

For each problem you need to identify

1. Number of half-lives

2. Starting amount (%, fraction, g, etc.)

3. Ending amount

4. Length of one half-life

5. Total amount of time to get from starting amount to ending amount

Wednesday, November 4th, 2015

What are the particles?

• Alpha

• Beta

•Gamma

• Positron

Examples – What goes where?!

• Sodium-23 undergoes beta decay

• Carbon-14 undergoes electron capture.

• A radioactive isotope goes through alpha decay to produce Nitrogen-14.

• Magnesium-24 is produced from the positron emission of an unstable isotope.

• The beta decay of Uranium-235 produces a gamma particle as well.

Sodium-23 undergoes beta decay

Carbon-14 undergoes electron capture.

A radioactive isotope goes through alpha decay to produce Nitrogen-14.

Magnesium-24 is produced from the positron emission of

an unstable isotope.

The beta decay of Uranium-235 produces a gamma

particle as well.

For each problem you need to identify

1. The reactant(s) 2. The

product(s)3. Total mass on the left of the arrow

4. Total mass on the right of the arrow

5. Total atomic number on the left of the arrow

6. Total atomic number on the right of the arrow