1. What fraction of nuclei remains in a radioactive sample after 4 half-lifes? 2
ID: 1617124 • Letter: 1
Question
1. What fraction of nuclei remains in a radioactive sample after 4 half-lifes?
2. The radioactive decay law describes the relationship between the initial number of nuclei N0 and the number of the nuclei remaining after time t:
N = N0 e-(lambda)t
Describe (quantitatively) the relationship between the half-life and the decay constant (lambda:)
T1/2 =
3. A radioactive sample is 90% decayed after how many half-lifes?
4. Write the radioactive decay law in terms of the half-life T1/2 instead of the decay constant (lambda:)
N/No = _________
Explanation / Answer
1.
N = N0*exp(-lambda*t)
lambda = 0.693/Thalf
N = N0*exp(0.693*t/Thalf)
after 4 half-lifes
N = N0*exp(-0.693*(4*Thalf)/Thalf)
N = N0*exp(-4*0.693)
N = 0.0625*N0
N/N0 = 0.0625
2.
from Q1
T1/2 = 0.693/lambda
3.
N = N0*exp(-0.693*t/Thalf)
90% decayed means
N = 0.1*N0
0.1*N0 = N0*exp(-0.693*t/Thalf)
ln (1/0.1) = 0.693*t/Thalf
t = (Thalf/0.693)*ln 10
t = 3.32*Thalf
4.
N/N0 = exp(-0.693*t/Thalf)
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