Question

a 20mg sample of thorium 233 decays to 17 mg after 5 min
a) determine the half life of thorium 233
b) How long will it take for this sample to decay to 1mg

Answer 1

How would i got about making an equation for this problem?

Answer 2

let r be the decay rate (time in minutes)
17 = 20 e^(5r)
0.85 = e^(5r)
ln 0.85 = 5r
similarly,
ln 0.5 = hr ... where h is the half-life,
so dividing the 2 equations,
ln 0.85 / ln 0.50 = 5r / hr = 5/h
h = 5 ln 0.50 / ln 0.85
h = 21.3 min

b)
1/20 = 0.05, so
ln 0.85 = 5r
ln 0.05 = tr
t = 5 ln 0.05 / ln 0.85
t = 92.2 min

Answer 3

how do you know when to use the "e"