Question

Select the correct answer.

A sample taken from a layer of mica in a canyon has 2.10 grams of potassium-40. A test reveals it to be 2.6 billion years old. How much
potassium-40 was in the sample originally if the half-life of potassium-40 is 1.3 billion years?
O A.
4.20 g
O B.
8.40 g
O C.
12.6 g
• D.
16.8 g
O E.
25.2 g

Answer 1

8.36 g

Step-by-step explanation:

From;

0.693/t1/2 = 2.303/t log (No/N)

t1/2 = half life of potassium-40

t = age of the sample

No= initial amount of the sample

N= amount of the sample at time t

Substituting values;

0.693/1.3 × 10^9 = 2.303/2.6 × 10^9 log (No/2.10)

5.33 × 10^-10 = 8.86 × 10^-10 log (No/2.10)

5.33 × 10^-10/8.86 × 10^-10 = log (No/2.10)

0.6 = log (No/2.10)

Antilog (0.6) = (No/2.10)

No = 2.10 × Antilog (0.6)

No= 8.36 g