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Earth Systems 3209. Reference: Chapters 6, 8; Appendix A & B. Unit: 2 Historical Geology . Unit 2: Topic 2.5. Radioactive Dating Problems. Focus on . . . d etermining the age of a sample using radiometric data.

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Earth Systems 3209

Reference:

Chapters 6, 8; Appendix A & B

Unit: 2Historical Geology

slide2

Unit 2: Topic 2.5

Radioactive Dating Problems

Focus on . . .

  • determining the age of a sample using radiometric data.
  • demonstrating scenarios that include calculations to determine;1) the fraction or percent of parent and daughter material,2) the number of half-lives,3) the ratios of parent to daughter materials, and 4) changing masses.
radioactive dating problems
Radioactive Dating Problems
  • These questions could make reference to the radioactive parent isotope in;
  • FractionForm (ex. 1/16th)
  • Percent Form (ex. 25%)
  • Remaining Parent in Grams (ex. 512 grams)
radioactive dating problems1
Radioactive Dating Problems
  • Note:When calculating any radioactive dating problem, you first need to calculate the number of half lives that has passed!!!
  • One piece of information given in the problem will allow you to do this.
  • Example:
  • Fraction (ex. 1/16th)
  • Percent (ex. 25%)
  • Ratio (1:7)
radioactive dating problems fraction
Radioactive Dating Problems (Fraction)

Problem Type #1: Fraction of parent material remaining

Given the half-life of U-235 is 0.7 billion years, determine the age of a sample of U-235 if 1/16 of the starting material remains.

Given:Half-life = 0.7 billion years

Fraction of parent (U-235) remaining = 1/16

  • You must first find out how many half-lives have passed if 1/16 of the parent (U-235) remains.

Age = # of Half-lives x Time for 1 Half-life

radioactive dating problems percent
Radioactive Dating Problems (Percent)

Problem Type #2: Percent of parent material remaining

Question:

Calculate the age of a rock using the K - 40 Ar – 40 dating method (which has a half – life of 1.3 billion years), if you know that 12.5% of the parent material now remains in the rock sample.

Information Given in Problem:

Half-life of radioactive sample  1.3 Billion Years

Parent material remaining  12.5%

radioactive dating problems percent1
Radioactive Dating Problems (Percent)

Problem Type #2: Percent of parent material remaining

The key to solving radioactive problems is that the number of half-lives (represented by “N”) must be found. To find the number of half-lives (N) that passed when 12.5% of the radioactive sample remains we can use a chart and follow the following steps:

  • Note:
  • The original amount before any radioactive material decayed was 100%
  • This is represented in the chart as zero half-lives.
  • Find how many half-lives the radioactive sample has to go through so that 12.5% remains.

After 3 half-lives Thus,“N” = ______

radioactive dating problems percent2
Radioactive Dating Problems (Percent)

Problem Type #2: Percent of parent material remaining

To calculate theAgeof the radioactive sample, use the following formula;

Age = “N” x # of years per half-life Where:

N = Number of half-livesAge = Half-life = 1.3 B.yrs.

Age =

radioactive dating problems mass remaining
Radioactive Dating Problems (Mass Remaining)

Problem Type #3: Mass of parent material remaining

1200 g of a radioactive element has decayed to produce 150 g of the element. If the half-life of the mineral is 0.40 billion years, what is the age of the sample?

Given: 1200 grams decays to 150 grams & Half-life = 0.4 Billion years

First find out how many half-lives have passed when 1200g decays to form 150g

# of Half LivesAge of Sample

Age = Number of HL X Time of HL

Age =

Age =

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Example 1:

What is the age of the rock described below?

(A) 2.6 billion years(B) 3.9 billion years

(C) 4.2 billion years(D) 5.5 billion years

A granite sample is dated using the radioactive isotope K-40, which has a half-life of 1.3 billion years. The rock contains 1/8 of the original K-40.

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Your Turn . . .

Take the time and complete the following questions . . .(Solutions to follow)

Question:

The half-life of element X is 200 000 years. If a sample originally held 256 g of parent isotope and the rock sample has been determined to be 1 million years old, what mass of parent now remains? Show calculations.

Given:

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Solutions . . .

Question:

  • The half-life of element X is 200 000 years. If a sample originally held 256 g of parent isotope and the rock sample has been determined to be 1 million years old, what mass of parent now remains? Show calculations.
  • Number of Half-lives:
  • Half-life = 1,000,000 years = 5 HL
  • 200,000 years
  • Mass of parent remaining:
  • 256g ➜ 128g ➜ 64g ➜ 32g ➜ 16g ➜ 8g
slide13

Your Turn . . .

Take the time and complete the following questions . . .(Solutions to follow)

Questions:

The parent isotope of a radioactive element has a half-life of 250 million years. If a sample contains 12.5% of the parent isotope, how old is the rock?Show all workings.

radioactive dating problems2
Radioactive Dating Problems

A “common error” students make when calculating this type of problem is;

  • Students when calculating the number of half-lives, as previously shown, count the “0" which implies 100% of the sample, as one of the half-lives.
  • This would give an incorrect number of half-lives (N = 4), which results in an incorrect answer.
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Summary . . .

Overview of Points covered:

  • First find the number of half lives.
  • Then you calculate the unknown, for example;
  • 1) Age
  • 2) Mass Remaining