Answered

A whalebone that originally contained 212 grams of C-14, half-life of 5700 years, now contains only 53 grams of C-14. How old is the whale bone?

A2850 years
B5700 years
C11400 years
D17100 years

Verified Answer :

JcAlmighty

The answer is C) 11400 years

Let's first calculate the remaining amount in percent:
212g is original amount or 100%.
53 g is x percents.
212 g : 100% = 53 g : x
x = 100% 53 g : 212 g
x = 25% = 0.25

Now, using the formula to calculate the number of half-lives:
(1/2)ⁿ = x,
where
x is the remaining amount: x = 0.25
n is the number of half-lives
1/2 stands for half-life.
(1/2)ⁿ = 0.25
⇒ nlog(1/2) = log(0.25) 
    n = log(0.25)/log(1/2) = log(0.25)/log(0.5) = -0.602/-0.301 = 2

The number of half-lives is 2.
Now, the number of half-lives (n) is a quotient of total time elapsed (T) and length of half-life (L):
n = T/L
We know:
n = 2
L = 5700 years
T = ?

Thus
T = L n
L = 5700 years 2
L = 11400 years

The answer is c) 11400 years

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