A rock sample from the moon includes a mineral that contains small amounts of the radioactive isotope Potassium- 40 and its daughter element Argon- 40 (half- life of 1.3 billion years). This mineral would not form with any Argon- 40. Consider a crystal with 7 atoms of Argon- 40 for every 1 atom of Potassium- 40. How long ago did this crystal form?

Question

Quizplus · Accepted Answer

Since the half-life of Potassium-40 is 1.3 billion years, for every 1 atom of Potassium-40 that decays, 1 atom of Argon-40 is produced. Therefore, if there are 7 atoms of Argon-40 for every 1 atom of Potassium-40, this means that 87.5% of the original Potassium-40 has decayed to produce the observed amount of Argon-40.

Using the formula for exponential decay: 
Fraction remaining = (1/2)^(time/half-life)

We can solve for the age of the crystal:

0.125 = (1/2)^(time/1.3 billion years)

Taking the logarithm of both sides:

log(0.125) = (time/1.3 billion years) * log(1/2)

Solving for time:

time = (log(0.125)/log(1/2)) * 1.3 billion years

time = 3.9 billion years

Therefore, the crystal formed 3.9 billion years ago.

A Rock Sample from the Moon Includes a Mineral That