20.2.2 Radiochemical Dating

Question 1

Radiochemical Dating

Answer 1

• Age of objects can be determined by using rates of radioactive decay for certain elements.
• The proportion of 14 C to 12 C in an object can be compared to the ratio in living things to determine how long ago a specimen died. The proportion of 238 U to 206 Pb can be used to determine when a rock was formed.

Question 2

note

Answer 2

• Given the half-life of a radioactive isotope, the amount of that isotope originally present, and the amount in the sample today, radioactivity can be used to determine the age of an object.
• Carbon-14 is used to date objects that were once alive. 14 C decays into atmospheric nitrogen-14.
• Other radioactive isotopes must be used to date inorganic objects. One commonly used method is uranium-238 dating. 238 U decays into 206 Pb.
• Rule of thumb: After about ten half-lives, virtually all of the starting substance will be gone.
• The 14 C amount today can be related to the original 14 C amount by the first order rate constant accounting for the time elapsed.
• While the plant is alive, carbon is continuously exchanged with the environment, which keeps the ratio constant. When the plant dies, no new carbon is incorporated. The amount of 14 C will decline.
• Comparing a contemporary sample producing 15
  disintegrations per minute with a sample of unknown age having 11 disintegrations per minute results in a ratio that can be used to indicate an approximate age for the sample.
• 238 U decays into 206 Pb, which is relatively rare. It is safe to assume that any lead-206 in a sample came from uranium-238.
• Problem: A rock contains 0.257 mg of 206 Pb for every mg of 238 U. How old is the rock?
• First, the mass of 206 Pb is converted to mass of 238 U. This results in a total of 1.297 mg 238 U originally for every 1.000 mg of 238 U currently present.
• Next, the known half-life of 238 U is used to calculate k (1.5 x 10 –10 y –1 ).
• These values are used to solve for the age of the rock (1.7 x 10 9 y).

Question 3

Which statement about radiocarbon dating is not correct?

Answer 3

The original reaction, which occurs in the atmosphere, is 14 6 C -> 14 7 N + 0 -1 e

Question 4

How old is an object whose current specific activity is 9.5 dpm/g? Remember that for a living organism, the specific activity is 15.3 dpm/g
For 14 7 C decay, t1/2 = 5,730

Answer 4

3,939 y

Question 5

Radiocarbon dating is a technique used by archaeologists and anthropologists to date specimens that were once alive. By making observations on the rate of radioactive decay for the following reactions, they can get a very accurate sense of the age of the specimen.
14 7 N + 1 0 n -> 14 6 C + 1 1 p
14 6 C -> 14 7 N + 0 -1 e
Which statement about radiocarbon dating is not correct?

Answer 5

The specific activity value fluctuates when an organism is alive because the 14 6 C is being exchanged with the atmosphere. When the organism dies, this value remains constant

Question 6

Radioactive isotope dating is used by archaeologists and anthropologists to date specimens that were never alive. This is especially true for geological dating. To do this, they make observations on the rate of radioactive decay for certain isotopes. We investigated such a decay by examining how 238U decays to 206Pb through a long series of beta and alpha decays. Which statement about this dating process is not correct?

Answer 6

ln (N / No ) = −k t½. However, the term (N / No ) is not directly related to the ratio of the current and original masses of 206Pb in the specimen.

Question 7

Which statement or expressions about 14 6 C dating is not correct?

Answer 7

t = 0.693/t1/2 * ln(A/Ao)

Question 8

Suppose that a piece of linen is discovered. Its current specific activity is 13.5 dpm/g. How old is the piece of linen?

Answer 8

1,035 y

Question 9

Which statement about carbon-14 is not correct?

Answer 9

When an organism dies, its equilibrium level for the radioactivity of 14 6 C becomes “locked” at a specific level

Question 10

Suppose that a rock contains 0.273 mg of 206Pb for every mg of 238U. If the current rock specimen contains 1.892 mg of 238U, how old is the rock specimen? (t½ of 238U = 4.5 × 109 y)

Answer 10

1.78 × 10^9 y

Question 11

Which statement about the radioactive decay of 238U is not correct?

Answer 11

Not all of the radioactive isotope 238U is unstable

Question 12

Which statement about carbon is not correct?

Answer 12

14C is a stable isotope. 12C and 13C are unstable isotopes.