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

Answer:

A = 0.75 gram or 1 gram

Step-by-step 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