Question

Complete the table for the radioactive isotope. (Round your answers to two decimal places.)

Isotope	Half-life (in years)	Initial quantity	Amount after 1000 years	Amount after 10,000 years
239Pu	24,100	?grams	grams	?0.4 grams

Answer 1

The table can be completed using the formula :

Nt = No(1/2)^{t / h}

where Nt is the amount of isotope left after time t

No is the initial sample amount

t is the time lapsed

and h is the half life period

So putting all the values for 10,000 years :

0.4 = No (1/2)^{10000 / 24100}

No = 0.53 grams

For 1000 years

Nt = 0.53 (1/2) ^{1000 / 24100}

Nt = 0.52 grams

isotope	half life	initial quantity	amount after 1000 years	amount after 10,000 years
239 Pu	24,100	0.53 grams	0.52 grams	0.4 grams