Answer:
c) 3.9 billion years
Explanation:
Hi there!
A given amount of a radioactive substance disintegrates over time. The time at which only half of the original amount remains is the half-life of the substance. Then, after one half-life, the amount of the substance will be half the original amount and after another half-life, the amount of the substance will be half of the halved amount, and so on.
Then, we have to find how many times the amount of potassium-40 halved.
If we initially have 40 g of potassium, after a half-life(1.3 billion years) there will be 20 g remaining. After another half-life (another 1.3 billion years), the remaining amount of potassium will be 10 g and after another half-life, it will be 5 g.
Then 3 half-lives were needed to reduce the amount of potassium in the rock from 40 to 5 g. Then, the rock is 3 half-lives old, that is 3 · 1.3 billion years = 3.9 billion years (answer c).
Mathematically you can express:
Initial amount/ 2ⁿ = remaining amount
Where n is the number of half-lives. In this case:
40 / 2ⁿ = 5
40/5 = 2ⁿ
8 = 2ⁿ
Apply logarithm
log(8) = log(2ⁿ)
Apply logarithm property: log(xᵃ) = a log(x)
log(8) = n log(2)
log(8)/log(2) = n
n = 3
Have a nice day!
