Multiple Choice
The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 20% of the U-238 atoms in a sample of U-238 to decay?
21. Nuclear Chemistry
Rate of Radioactive Decay
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How many mg of a 3.50-mg sample of Tc-99 will remain after 4 half-lives have passed?
A
0.0550 mg
B
0.109 mg
C
0.219 mg
D
0.438 mg
E
0.875 mg
Verified step by step guidance1
Understand that the problem involves radioactive decay, specifically the decay of Tc-99, which follows first-order kinetics characterized by its half-life.
Recall that the half-life of a substance is the time required for half of the sample to decay. After one half-life, 50% of the original sample remains.
Calculate the fraction of the sample remaining after 4 half-lives using the formula: \( \text{Remaining fraction} = \left( \frac{1}{2} \right)^n \), where \( n \) is the number of half-lives.
Substitute \( n = 4 \) into the formula to find the fraction of the sample remaining after 4 half-lives.
Multiply the initial mass of the sample (3.50 mg) by the fraction calculated in the previous step to determine the mass of Tc-99 remaining after 4 half-lives.
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