Question

If an Egyptian mummy contained 10 g of carbon-14 when it was buried and now has 5 g, how old is the mummy?

How many grams of nitrogen -14 were produced during that time?
In another six thousand years, how much carbon-14 will remain?
What would be the total amount of nitrogen-14 produced in twelve thousand years after the burial of the mummy?​

Answer 1

Age of mummy when 5 g carbon-14 remains = 6000 years

nitrogen-14 produced during this period = 5 g

Mass of Carbon 14 in another 6000 years = 2.5 g

Amount of Nitrogen-14 in 12 thousand years = 7.5 g

Step-by-step explanation:

Carbon dating is a method used for age determination by analyzing the decay

of carbon-14 to nitrogen-14

`^(14)C ---> ^(14)N + \beta ^(-)`

one neutron in carbon-14 splits into one proton and electron

half life (time to decay half of the total mass) of carbon-14 is 5730. here we can approximate this as 6000 years.

initially there is 10 g carbon-14 now remains 5 g that means 1 half-life has passed so,

Age of mummy when 5 g carbon-14 remains = 6000 years

the decayed C-14 is converted to N-14 ( mass of electrons or β particles are negligible) so,

nitrogen-14 produced during this period = (10 - 5 = 5 g

in another 6000 year one more half life will pass the mass of C-14 will further halve ,

Mass of Carbon 14 in another 6000 years = 5 / 2 = 2.5 g

so, Nitrogen remains after 12000 years = 10 - 2.5 = 7.5 g