Question

Carbon-14 emits beta radiation and decays with a half-life (t) of 5730 years. Assume that you start with a mass of 6000 g of carbon 14. How many grams of the isotope remains at the end of four half-lives?

Answer 1

375g of a carbon-14 isotope

Step-by-step explanation:

From

N/No = (1/2) t/t1/2

N= mass of isotope remaining after time (t)

No= mass of isotope present at the beginning

t= time taken for mass of isotope to decrease to N

t1/2= half life of the isotope.

Since 1 half-life= 5730 years= t1/2

Four half lives= 4(5730) years= t

No= 6000g of isotope

Then we substitute into the formula

N/6000 = (1/2)^4(5730)/5730

N/6000 = (1/2)^4

N= (1/2)^4 ×6000

N= 375g of a carbon-14 isotope