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OB: nuclear chem class #2 practice decay reactions, the half life of radioisotopes.

OB: nuclear chem class #2 practice decay reactions, the half life of radioisotopes

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OB: nuclear chem class #2practice decay reactions, the half life of radioisotopes

A half life is the amount of time it takes for one half of a given radioisotope to transmute. Which half, even which atoms will actually decay is a mystery. But, statistically, half will transmute in a given half life.

First, let’s practice the decay reactions for these isotopes…

19879

Au

146

C

13153

I

23994

Pu

23892

U

3720

Ca

First, let’s practice the decay reactions for these isotopes…

19879

Gold-198 undergoes beta decay and transmutes to mercury-198

Au

0-1

e

19880

+

Hg

147

N

146

C

0-1

e

+

Carbon-14 transmutes to N-14 by beta decay.

13153

I

0-1

e

+

13154

Xe

Iodine-131 becomes Xe-131 by beta decay.

23994

Pu

42

+

23592

Pu-239 transmutes into U-235 by alpha decay.

He

U

42

Alpha decay occurs and uranium-238 becomes thorium-234.

23892

He

23490

U

+

Th

3720

Ca

+

3719

K

Calcium-37 undergoes positron decay and forms into potassium-37.

0+1

e

HALF LIFE: the amount of time it takes for one half of a radioisotope to decay into a daughter isotope.

The details of why this occurs or how this occurs, or even when any particular isotope will decay is unknown. What is known very well is the amount of time it takes for these isotopes to decay. Statistics are easy compared to looking at individual atoms.

Some half lives of isotopes are very, very long, in the millions of years.

Some isotopes have half lives measured in milliseconds (thousandths of a second).

Many half lives are listed in table N, let’s look now…

The half life of radioactive gold-198 is 2.69 days.

This means that if you have 150.0 grams of Au-198, in 2.69 days you will have just 75.00 grams of this isotope, and 75.00 grams of what ever it is that it transmuted into (Hg-198)

In 2.69 more days, you will have just 37.50 grams of the radioactive gold, and 37.50 more grams of the mercury.

After yet another 2.69 days, you’ll have only 18.75 grams of your gold. Each half life passes and another half of the radioactive isotope decays away.

The beta decay of gold-198

Mass

150.0 g

75.00 g

37.50 g

18.75 g

2

3

0

1

Half Lives

Total time passed: 2.695 days 5.390 days 8.085 days

In our class the half lives will always be whole numbers, we will not measure these in partial half lives. The math is easy in high school.

You accumulate 22.0 grams of the radioisotope carbon-14. How long before you have only 2.75 grams?

Every single half life problem demands that you draw a timeline.Every single one, even this one.

22.0 g

0 half lives

You accumulate 22.0 grams of the radioisotope carbon-14. How long before you have only 2.75 grams?

22.0 g

5.50 g

2.75 g

11.0 g

0 half lives

1 half life

3 half lives

2 half lives

It takes the length of time of three half lives for 22.0 g of Carbon-14 to transmute into just 2.75 grams. Since each half life of this radioisotope is 5715 years,

5715 years X 3 = 17,145 years

It will take 17,145 years for this to happen.

The doctor wants to inject you with some radioactive Iodine-131 to measure your thyroid uptake. She injects you with 2.00 grams. How long until you have just 0.03125 g left in you? (disregard the significant figures here)

2.00 g

0 half lives

Start your timeline, and watch the calculator buttons. Go slowly.

The doctor wants to inject you with some radioactive Iodine-131 to measure your thyroid uptake. She injects you with 2.00 grams. How long until you have just 0.03125 g left in you? (disregard the significant figures here)

2.00 g

1.00 g

0.500 g

0.250 g

0.125 g

0.0625 g

0.03125 g

0 half lives

1

2

3

4

5

6

It will take 6 half lives for this 2.00 g radioactive iodine to transmute away so that only 0.03125 g remains. Each half life is 8.07 days, so…

6 X 8.021 days = about 48.126 days, about 1½ months.

You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo?

400.0 g

0 half lives

The easy stuff first, then the math…

Iron-53 undergoes positron decay this way:

You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo?

400.0 g

0 half lives

The easy stuff first, then the math…

Iron-53 undergoes positron decay this way:

This is positron decay.

5326

0+1

e

+

5325

Mn

Fe

You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo?

400.0 g

200.0 g

100.0 g

50.0 g

25.0 g

12.5 g

1 2 3 4 5

0 half lives

5 half lives must pass for this to happen. Each half life of Iron-53 is 8.51 minutes.

8.51 minutes X 5 = 42.55 minutes (let’s round that to 43 minutes)

So… it will be about 12:43 PM