Question

A geologist is studying two different rhyolite flows to determine if they were erupted at the same time.

9)Rhyolite #1 has 50% of the parent Isotope F remaining. How many half lives have occurred?
10)Rhyolite #2 has 75% Daughter G and 25% parent H. How many half lives has the rock gone through?
11)Parent Isotope F in the first question has a half life of 100 million years. Use your answer from question 9 to determine the age of rhyolite#1.

Answer 1

Q1. The answer is 1.

It can be calculated using the equation:

 (1/2)ⁿ = x

x - decimal amount remaining, 

n - a number of half-lives.

x = 50% = 50/100 = 0.5

n = ?

(1/2)ⁿ = 0.5

log((1/2)ⁿ) = log(0.5)

n * log(1/2) = log(0.5)

n * log(0.5) = log(0.5)

n = log(0.5)/log(0.5)

n = 1

Q10. The answer is 2.

It can be calculated using the equation:

 (1/2)ⁿ = x

x - decimal amount remaining, 

n - a number of half-lives.

Rhyolite #2 has 25% of the parent H remaining:

x = 25% = 25/100 = 0.25

n = ?

(1/2)ⁿ = 0.25

log((1/2)ⁿ) = log(0.25)

n * log(1/2) = log(0.25)

n * log(0.5) = log(0.25)

n = log(0.25)/log(0.5)

n = -0.602 / - 0.301

n = 2

Q3. The answer is 100 million years.

A number of half-lives (n) is a quotient of total time elapsed (t) and length of half-life (H):

n = t/H

n = 1

t = ?

H = 100 000 000 years

n = t/H

t = n * H

t = 1 * 100 000 000 years

t = 100 000 000 years