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2 years ago

How old is a bone if it now .3125 of C-14 when it originally had 80.0g of C-14

Chemistry

1 answer:

Taya2010 [7]2 years ago

7 0

<h3>Answer:</h3>

42960 years

<h3>Explanation:</h3>

<u>We are given;</u>

Remaining mass of C-14 in a bone is 0.3125 g
Original mass of C-14 on the bone is 80.0 g
Half life of C-14 is 5370 years

We are required to determine the age of the bone;

Using the formula;

Remaining mass = Original mass × 0.5^n , where n is the number of half lives.

Therefore;

0.3125 g = 80.0 g × 0.5^n

3.90625 × 10^-3 = 0.5^n

Introducing logarithm on both sides;

log 3.90625 × 10^-3 = n log 0.5

Solving for n

n = log 3.90625 × 10^-3 ÷ log 0.5

= 8

Therefore, the number of half lives is 8
But, 1 half life is 5370 years
Therefore;

Age of the rock = 5370 years × 8

= 42960 years

Thus, the bone is 42960 years old

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