Concept explainers
Consider two 100-gram samples of radium-226 and uranium-238. Rank by the amount left of each.
(A) radium after 1620 years
(B) uranium after 2 half-lives
(C) radium after 3 half-lives
(D) uranium after 1 half-life
The rank of radioactive element by left amount of the Uranium and Radium.
Explanation of Solution
Introduction:
The amount of the radioactive elements becomes half the initial amount in the duration equal to the half-life of the radioactive element.
The half-life of radium is 1620 years. So, the amount becomes 50 gram in the sample of radium-226.
The amount of the uranium after two half-life becomes one-fourth of the initial amount. So, the 25 grams uranium is left in the sample of uranium-238.
The amount of the radium after three half-life becomes one-eighth of the initial amount. So, the 12.5 grams radium is left in the sample of radium-226.
The amount of the uranium after one half-life becomes half of the initial amount. So, the 50 grams uranium is left in the sample of uranium-238.
Conclusion:
Thus, the rank of samples by the amount of radioactive material left is A = D, B, C.
Chapter 39 Solutions
Conceptual Physics: The High School Physics Program
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