The half-life of carbon 14 is 5, 730 years. How much would be left of an original 50- gram sample after 2, 292 years?

Given :

The half-life of carbon 14 is 5,730 years.

To Find :

How much would be left of an original 50- gram sample after 2, 292 years.

Solution :

We know, rate law for first order reaction is given by :

  ...1)

Here, is initial amount and is final amount.

And

Putting value of half time in above equation, we get :

Putting value of k in equation 1) , we get :

Hence, this is the required solution.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2