The half-life of polonium-218 is 3.0 minutes. If you start with 30.0 g, how long will it be before only 2.0 g remains?

Question

The half-life of polonium-218 is 3.0 minutes. If you start with 30.0 g, how long will it be before only 2.0 g remains?

Answer 1

Fraction remaining = 0.5ⁿ where n = # of half lives elapsed

Fraction remaining = 2.0 g/30.0 g = 0.06667

0.06667 = 0.5ⁿ

log 0.06667 = n log 0.5

n = 3.907 half lives

3.907 half lives x 3.0 min/half life = 11.7 minutes

Answer 2

30 initially,

15 in 3 minutes ,

7.5 in 6 minutes ,

3.75 in 9 minutes ,

1.875 in 12 minutes

2 in maybe about 11 minutes