Question

The radioisotope radon-222 has a half life of 3.8 days. How much of a 65-g sample of radon-222 would be left after approximately 15 days? Show all work. I REALLY NEED HELP!

Answer 1

Answer: 4.2 g


Step-by-step explanation:

1) Radioisotope decay formula:


`N=N_0e^(-rt)`


2) Half-life formula

Replace N = No / 2 and solve for r



`(1)/(2) =e^(-rt)`


`r=ln2/t`

3) Replace with t = 3.8

r = ln2 / 8 = 0.1824

4) Apply the equation with No = 65g, r = 0.1824, and t = 15

N = 65g × e ^ (-0.1824 × 15) = 4.2 g

You can reasoning whether that answer makes sense:

1 half life = 3.8 days

⇒ After 3.8 days half of the mass left is 65g / 2 = 32.5 g

⇒ After other 3.8 days (a total of 7.6 days) half of 32.5 g is 16.25 g

⇒ After other 3.8 days (a total of 11.4) half of 16.25g = 8.125 g

⇒ After other 3.8 days (a total of 15.2) half of 8.125g = 4.06 g

As you see indeed 15 days is almost 4 half-lives time and so the mass remaining is close to 4.06 grams.