(a)
The number of atoms of radioactive substance with half-life 12 minutes and initial number of atoms of
(a)
Answer to Problem 8E
The number of atoms of the element after 48 minutes are
Explanation of Solution
Given info: The initial number of atoms are
Half-life of a radioactive element is the time taken by the element to decay into half of its initial amount. It is represented by
Let n be the number of half-life involved in the decay of a radioactive element.
Write the expression for the number half-life.
Here,
Substitute
In each half life, half portion of amount decays. Therefore write the fraction of initial element remaining after 4 half-life.
Therefore, write the expression for the number of atoms decayed after
Here,
Substitute
Conclusion:
The number of atoms of the element after 48 minutes are
(b)
The number of atoms of radioactive substance with half-life 12 minutes and initial number of atoms of
(b)
Answer to Problem 8E
The number of atoms of the atoms remain after 1 hour 24 minutes
Explanation of Solution
Given info: The initial number of atoms are
Write the expression for the number half-life.
Convert 1 hour 24 minutes into minutes.
Substitute
In each half life, half portion of amount decays. Therefore write the fraction of initial element remaining after 7 half-life.
Therefore, write the expression for the number of atoms decayed after
Substitute
Conclusion:
The number of atoms of the atoms remain after 1 hour 24 minutes
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Chapter 19 Solutions
Physics of Everyday Phenomena
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