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

Step-by-step 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=(0.693)/(t_(1/2))`

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

`k=1.21* 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=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant =
`1.21* 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=(2.303)/(1.21* 10^(-4))\log(10)/(a-x)`

`a-x=2.5g`

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