How many half-lives for activity to fall below 0.1%?

[dagg3r]

Radioactive materials are considered to be relatively safe when their activity has fallen below 0.1% of their initial value.
a How many half-lives does this take?

a 0.1% = 0.001, and 1/2^n = 1/1000
n = 10 or 10 half-lives

how did they get n=10

 

[Alexander]

2^-x = 0.001, so taking logarithm of both sides you get x = -log₂(0.001) = 3log₂(10)=3/log₁₀(2)=3/0.301 = 9.97 = 10