The half-life of ruthenium-106 is 1 year. If an original sample of ruthenium-106 had a mass of?

Question

If an original sample of ruthenium-106 had a mass of 128 mg, and there are 2 mg left, what is the elapsed time?

Answer 1

a(naught)e^rt
128e^-1t
(-1t)ln(128)
i dont have a calculator but u can finish it from there

Answer 2

Using the half life formula:

Amount Remaining = Initial Amount (2)^-(t / hl)
(it can also be written as (0.5)^(t / hl), but it easier to take a shortcut if you write it as 2 ^ -(t/hl))

2 = 128 (2)^-(t / 1)
2 / 128 = 2^-t
1/64 = 2^-t
If you know that 1 / 64 is equal to 2^-6, you can take a shortcut.
2^-6 = 2^-t
-6 = -t
t = 6 years

If you don't, take the log of both sides
log (1 / 64) = log (2^-t)
Using the power law
log (1 / 64) = -t(log2)
log(1 / 64) / log2 = -t
t = 6 years

Answer 3

A=Ao (0.5^(t/1))

A= final mass
Ao= initial mass
t= time elapsed
1= half life

2= 128 (0.5^t)
0.015625= 0.5^t
log both sides
log0.015625 = t log0.5
t= log0.015625/log0.5
=6