Answer:
2.2 % and 0 %
Explanation:
The equation we will be using to solve this question is:
N/Nā Ā = eā»Ī» t
where Ā Nā : Number of paricles at t= 0
Ā Ā Ā Ā Ā Ā N= Ā Number of particles after time t
Ā Ā Ā Ā Ā Ā Ā Ī»= Radioactive decay constant
Ā Ā Ā Ā Ā Ā Ā e= EulerĀ“s constant
We are not given Ī» , but it can be determined from the half life with the equation:
Ī» = 0.693 / t 1/2 where t 1/2 is the half-life
Substituting our values:
Ī» = 0.693 / 55 s = 0.0126/s
a) For t = 5 min = 300 s
N / Nā = e^-(0.0126/s x 300 s) = e^-3.8 = 0.022 = 2.2 %
b) For t = 1 hr = 3600 s
N / Nā = Ā e^-(0.0126/s x 3600 s) = 2.9 x 10 ā»Ā²ā° = 0 % (For all practical purposes)
