Answer :
Potassium- 40 has a half-life of 1.27 x 10⁹ years. You have a modern sample that now has 97.3% of the amount you expected your sample had at the start. The age of the sample is 3.43 billion years old.
The half-life of potassium-40 is 1.27 x 10⁹ years. This means that half of the potassium-40 atoms in a sample will decay after 1.27 x 10⁹ years.
Calculate the percentage of potassium-40 atoms that have decayed:
percentage decayed = 1 - 97.3 = 2.7
If your sample now has 97.3% of the amount of potassium-40 that it had at the start, then this means that 2.7% of the potassium-40 atoms have decayed.
Calculate the number of half-lives that have passed:
number of half lives = percentage decayed / 0.5 = 2.7 / 0.5 = 5.4
Calculate the age of the sample:
age = number of half lives * half-life = 5.4 * 1.27 x 10⁹ = 3.43 x 10⁸ years
Since half of the potassium-40 atoms will decay after 1.27 x 10⁹ years, then 2.7% of the potassium-40 atoms will decay after 3.43 x 10⁸ years.
Therefore, the age of the sample is 3.43 billion years old.
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The complete question is:
Potassium- 40 has a half-life of 1.27 x 10⁹ years. You have a modern sample that now has 97.3% of the amount you expected your sample had at the start. How old is your sample?
