Question

A rock is believed to have been formed 1.25 billion years ago, as calculated by using potassium-40 dating. If the half-life of potassium-40 is 1.25 billion years, what percentage of the original amount of potassium-40 was found in this sample of rock?

Answer 1

Answer:

The answer to the question is

50 % of the original amount of potassium 40 will be left after one half life or 1.25 billion years

Explanation:

To solve the question we note that the half life is the time for half of the quantity of  substance that undergoes radioactive decay to  disintegrate, thus

we have

half life of potassium 40 K₄₀ = 1.25 billion years

To support the believe tht the rock was formed 1.25 billion years ago we have

$N_{(t)} =N_{(0)} (\frac{1}{2}) ^{\frac{t}{t_{\frac{1}{2} } } }$

After 1.25 billion years we have

$N_{(t)} =N_{(0)} (\frac{1}{2}) ^{\frac{1.25billion}{1.25 billion} } } }$  = $N_{(t)} =N_{(0)} (\frac{1}{2}) ^{1 } } }$ =0.5 of $N_{(0)}$ will be left or 50 % of the original amount of potassium 40 will be left