Question

The half-life of carbon-14 is 5730 if you start with 10 grams and 11,460 years passed by how many grams of carbon-14 will be remaining???
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Answer 1

Answer:

Explanation:

Answer 2

Answer : The amount of carbon-14 remaining will be, 2.5 grams.

Explanation :

Half-life = 5730 years

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{5730\text{ years}}$

$k=1.21\times 10^{-4}\text{ years}^{-1}$

Now we have to calculate the time passed.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  = $1.21\times 10^{-4}\text{ years}^{-1}$

t = time passed by the sample  = 11460 years

a = initial amount of the reactant  = 10 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

$11460=\frac{2.303}{1.21\times 10^{-4}}\log\frac{10}{a-x}$

$a-x=2.5g$

Therefore, the amount of carbon-14 remaining will be, 2.5 grams.