Question

A 500. gram sample of nickle-63 has a half-life of 100. years and has decayed for 500. years. How much of the original 500. gram sample remains?

87.1 grams
574 grams
16,000 grams
15.6 grams

Answer 1

Halve it five times:
250
125
62.5
31.25
15.6
ta-da

Answer 2

15.6 gram

Step-by-step explanation:

half life, T = 100 years

initial amount, No = 500 g

decay time, t = 500 years

number of half lives, n = t / T = 500 / 100 = 5

Amount of substance remaining in the sample is given by

`=N_(o)\left ( (1)/(2) \right )^(n)`

where, n be the number of half lives, No be the initial amount, N be the remaining amount in the sample

So,

`N=500\left ( (1)/(2) \right )^(5)`

N = 15.6 g

Thus, the amount of remaining substance after 500 years is 15.6 g.