MU #1 Each radioactive isotope has a specific rate of decay (half-life).

The half-life of a radioactive substance is the time it takes for half of an initial amount of the substance to decay.  The half-live  is independent of chemical activity, external pressure, and temperature. See table N

Example

Consider a 10 g sample of Au-198 (half-Life of 2.69 days)

After 0 half-life or 0 days 10 g are present.

After 1 half-life or 2.69 days 5 g remains.

After 2 half-life or 5.38 days (2 x 2.69 days) 2.5 g remains.

After 3 half-life or 8.07 days (3 x 2.69 days) 1.25 g remains.

The graph below represents the 10 g of Au-198 through 6 half-lives.

This table is very useful to solve simple half-live problems.

The formula to calculate the fraction remaining is in table T

fraction remaining = (1/2)^t/T

t = total time elapsed

T = half-life

number of half-life periods = t/T

The formula to calculate the mass of the sample remaining is

mass of sample remaining = (1/2)^t/T (mass of original sample)

Example

Consider a 100g sample of C-14. (C-14 decays into N-14)

After 0 half-life or 0 years there will be 100 g of C-14 and 0 g of N-14 (the decay product)

    fraction of C-14 remaining = (1/2)^0/5730 (100g) = (1/2)⁰ (100g) = 100g

After 1 half-life or 5730 years there will be 50 g of C-14 and 50 g of N-14

    fraction of C-14 remaining = (1/2)^5730/5730 (100g) = (1/2)¹ (100g) = 50g

After 2 half-life or 2(5730 years) there will be 25 g of C-14 and 75 g of N-14

    fraction of C-14 remaining = (1/2)^11460/5730 (100g) = (1/2)² (100g) = 25g

After 3 half-life or 3(5730 years) there will be 12.5 g of C-14 and 87.5 g of N-14

    fraction of C-14 remaining = (1/2) ^17190/5730 (100g) = (1/2)³ (100g) = 12.5g

Example

What will remain of a 50 g sample of phosphorus-32 after 1716 hours?

Solution

Mass of original sample = 50 g

T = 14.3 d

t = 1716 hours or 71.5 d

fraction remaining = (1/2)^t/T = (.5)^{71.5 d/14.3 d} = (.5)⁵ = (.5) (.5) (.5) (.5) (.5) = 0.03125

mass of P-32 remaining =  (1/2)^t/T (mass of original sample) = (0.03125) (50g) = 1.56 g

TEST YOUR UNDERSTANDING

8/07

81 The fossilized remains of a plant were found at a construction site. The fossilized remains contain 1/16 the amount of carbon-14 that is present in a living plant. Determine the approximate age of these fossilized remains.

1/07

6/02 Exactly how much time must elapse before 16 grams of potassium-42 decays, leaving 2 grams of the original isotope?

            (1) 8 x 12.4 hours   (2) 2 x 12.4 hours   (3) 3 x 12.4 hours        (4) 4 x 12.4 hours

6/02 As a sample of the radioactive isotope ¹³¹I decays, its half-life  (1) decreases    (2) increases  (3) remains the same

8/03

50 According to Reference Table N, which radioactive isotope will retain only one-eighth its original radioactive atoms after approximately 43 days? (1) gold-198 (2) iodine-131 (3) phosphorus-32 (4) radon-222

1/04

47 After 32 days, 5 milligrams of an 80-milligram sample of a radioactive isotope remains unchanged. What is the half-life of this element?
        (1) 8 days (2) 2 days (3) 16 days (4) 4 days

6/04

49 Based on Reference Table N, what fraction of a sample of gold-198 remains radioactive after 2.69 days? (1) 1/4 (2) 1/2 (3)3/4 (4) 7/8

8/04

Base your answers to questions 82 through 85 on the reading passage below and on your knowledge of chemistry.

A Glow in the Dark, and Scientific Peril

                The [Marie and Pierre] Curies set out to study radioactivity in 1898. Their first accomplishment was to show that radioactivity was a property of atoms themselves. Scientifically, that was the most important of their findings; because it helped other researchers refine their understanding of atomic structure.

                More famous was their discovery of polonium and radium. Radium was the most radioactive substance the Curies had encountered. Its radioactivity is due to the large size of the atom, which makes the nucleus unstable and prone to decay, usually to radon and then lead, by emitting particles and energy as it seeks a more stable configuration.

                Marie Curie struggled to purify radium for medical uses, including early radiation treatment for tumors. But radium’s bluish glow caught people’s fancy, and companies in the United States began mining it and selling it as a novelty: for glow-in-the-dark light pulls, for instance, and bogus cure-all patent medicines that actually killed people.

                What makes radium so dangerous is that it forms chemical bonds in the same way as calcium, and the body can mistake it for calcium and absorb it into the bones. Then, it can bombard cells with radiation at close range, which may cause bone tumors or bone-marrow damage that can give rise to anemia or leukemia.

— Denise Grady, The New York Times, October 6, 1998

82 State one risk associated with the use of radium.

83 Using Reference Table N, complete the equation provided in your answer booklet for the nuclear decay of 226-Ra. Include both atomic number and mass number for each particle.

84 Using information from the Periodic Table explain why radium forms chemical bonds in the same way as calcium does.

85 If a scientist purifies 1.0 gram of radium-226, how many years must pass before only 0.50 gram of the original radium-226 sample remains unchanged?

1/05

49 Based on Reference Table N, what fraction of a radioactive 90-Sr sample would remain unchanged after 56.2 years? (1) 1 (2) 1 (3)1  (4)16

6/05

29 What is the half-life and decay mode of Rn-222?

                    (1) 1.91 days and alpha decay (2) 1.91 days and beta decay (3) 3.82 days and alpha decay (4) 3.82 days and beta decay

6/06

8/06

home