Modern Physics 7 Question 44

49. 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 4.16yr, the value of p is

(2010)

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Answer:

Correct Answer: 49. 850. Atomic number, mass number

Solution:

  1. dNdt=∣ Activity of radioactive substance

=λN=λN0eλt

Taking log both sides

lndNdt=ln(λN0)λt

Hence, lndNdt versus t graph is a straight line with slope λ.

From the graph we can see that, λ=12=0.5yr1

Now applying the equation,

N=N0eλt=N0e0.5×4.16=N0e2.08=0.125N0=N08

i.e, nuclei decreases by a factor of 8 .

Hence, the answer is 8.



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