Question

The half-life of carbon 14 is years. How much would be left of an original -gram sample after 2,292 years? (To the nearest whole number)

Answer 1

A = 0.75 gram or 1 gram

Explanation:

The half-life of carbon 14 is years. How much would be left of an original -gram sample after 2,292 years? (To the nearest whole number).

We can use the following formula for half-life of
`^(14)C` to find out how much is left from the original sample after 2,292 years:

`A = A_(0)e^(-0.000124t)`

where:

A is the amount left of an original gram sample after t years, and

`A_(0)` is the amount present at time t = 0.

The half-life of
`^(14)C` is the time t at which the amount present is one-half the amount at time t = 0.

If 1 gram of
`^(14)C` is present in a sample,

Solve for A when t = 2,292:

Substituting
`A_(0)` = 1 gram into the decay equation, and we have:

`A = A_(0)e^(-0.000124t)`

`A = A_(0)e^(-0.000124(2,292))`

A = 0.75 g or 1 g