Question

Measurement of a certain element in a sample rock shows that it contains one-fourth (1/4) of the original amount. If the half-life of the original element is 25 million years, how old is the rock?

(a) 25÷4 million years
(b) 25 million years
(c) 50 million years
(d) 75 million years
(e) 100 million years

Answer 1

To determine the rock's age, we consider that after two half-lives, one-fourth of the original element remains. Since each half-life is 25 million years, two half-lives would total 50 million years, which is the age of the rock.

Step-by-step explanation:

To determine the age of the rock using the concept of half-lives, we identify that after one half-life, half of the original element remains, after two half-lives, one-fourth (or one half of the remainder) is left. Since the half-life of the element is given as 25 million years, and we're told the rock contains one-fourth of the original element, we can infer that two half-lives must have passed.

Calculating the age involves multiplying the number of half-lives by the duration of one half-life:

• 1st half-life: 25 million years (50% remains)
• 2nd half-life: + 25 million years (25% remains)

The sum is 50 million years, so the rock is approximately 50 million years old (Option (c)).