Question

5 grams of chucknorrisidium created, decays at a half-life of 16,000,000 Need 1 gram for experiments. How long before the is 1 gram remaining

Answer 1

the time taken for the element to remain 1 gram is 38,400,000 unit.

Explanation:

Given;

initial mass, m = 5 g

half life, t = 16,000,000 unit

The time taken for the element to remain 1 gram is calculated as;

mass remaining time

5 g 0

2.5 g 16,000,000

1.25 g 32,000,000

0.625 g 48,000,000

Interpolate to obtain the time at 1 gram;

1.25 g ---------------------------------- 32,000,000

1 g --------------------------------------------- x

0.625 g --------------------------------------- 48,000,000

`(1.25 - 1)/(1.25 - 0.625) = (32,000,000 - x)/(32,000,000 - 48,000,000) \\\\(0.25)/(0.625) = (32,000,000 - x)/(-16,000,000) \\\\-4,000,000= 20,000,000 - 0.625x\\\\0.625x = 20,000,000 + 4,000,000\\\\0.625x = 24,000,000\\\\x = (24,000,000)/(0.625) \\\\x = 38,400,000`

Therefore, the time taken for the element to remain 1 gram is 38,400,000 unit.