Answer:
t = 66.4 minutes ( to the nearest tenth of a minute)
it would take the element 66.4 minutes to decay to 11 grams
Step-by-step explanation:
Given;
Initial amount N = 510 g
Final amount Nt = 11 g
Half life t(1/2) = 12 minutes
The amount of time t required for the Element X to decay from N to Nt can be written as;
t = ln(Nt/N) ÷ -λ .....1
Where;
λ = decay constant
λ = ln(2)/t(1/2)
Substituting λ, equation 1 then becomes;
t = ln(Nt/N) ÷ -(ln(2)/t(1/2))
Substituting the values;
t = ln(11/510) ÷ -(ln(2)/12)
t = −3.8365 ÷ -0.05776
t = 66.419
t = 66.4 minutes ( to the nearest tenth of a minute)
