Concept explainers
(a)
The activity of the radioactive nuclide after
(a)
Answer to Problem 38P
The activity of the radioactive nuclide after
Explanation of Solution
A radioactive nuclide has half-life
Write the formula for half-life
Here,
Write the formula for the activity
Here,
Conclusion:
Substitute equation (I) in (II) and rewrite to find the
Substitute
Thus, the activity of the radioactive nuclide after
(b)
The initial number of nuclei in a radioactive sample.
(b)
Answer to Problem 38P
The initial number of nuclei in a radioactive sample is
Explanation of Solution
Write the formula for the activity
Here,
Write the formula for the number of nuclei
Here,
Write the formula for the time constant
Conclusion:
Substitute equation (II) and (IV) in (III) and rewrite to find
Substitute equation (V) and (I) in above equation
Substitute
Thus, the initial number of nuclei in a radioactive sample is
(c)
The probability per second of any one of the nuclei decay.
(c)
Answer to Problem 38P
The probability per second of any one of the nuclei decay is
Explanation of Solution
Substitute equation (I) in (V) and solve for
Substitute
Thus, the probability per second of any one of the nuclei decay is
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Chapter 29 Solutions
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