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Question:

To determine the half-life of a radioactive element, a student plots a graph of ln|dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is:

10

11

8

9

Solution:

N=N0e−λt
ln|dN/dt|=ln(N0λ)−λt
From graph, λ=1/2 per year
t1/2=0.693/λ=1.386 year
4.16 yrs = 3t1/2
∴p=8