A chemist determines that a sample of petrified wood has a carbon-14 decay rate of 6.00 counts per minute per gram. The decay rate of carbon-14 in fresh wood today is 13.6 counts per minute per gram, and the half life of carbon-14 is 5730 years. What is the age of the piece of wood in years?

6,765 years

Explanation:

Calculation to determine the age of the piece of wood in years

First step is to calculate decimal fraction of Carbon-14 that was remaining

Decimal fraction of Carbon-14= 6.00 counts per minute per gram/ 13.6 counts per minute per gram

Decimal fraction of Carbon-14 remaining= 0.4411765

Second step is to calculate the numbers of half-lives that have elapsed

(1/2)^n= 0.4411765

Hence,

n log 0.5 = log 0.4411765

n = 1.18057

Last step is to calculate the length of time that has elapsed

Using this formula

Elapsed length of time=Half life of carbon-14 *n

Let plug in the formula

Elapsed length of time=5,730 years * 1.18057

Elapsed length of time= 6,765 years

Therefore the age of the piece of wood in years will be 6,765 years

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3