Multiple Choice
What is the half-life of the radioisotope that shows the following plot of remaining percentage vs. time?
17. Radioactivity and Nuclear Chemistry
Radioactive Half-Life
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The half-life of arsenic-74 is about 18 days. If a sample initially contains 100.00 mg arsenic-74, what mass (in mg) would be left after 72 days?
A
0.0625 mg
B
6.25 mg
C
25 mg
D
12.5 mg
E
50 mg
Verified step by step guidance1
Understand the concept of half-life: The half-life of a radioactive isotope is the time required for half of the isotope to decay. For arsenic-74, this is 18 days.
Determine how many half-lives have passed in 72 days: Divide the total time (72 days) by the half-life (18 days) to find the number of half-lives.
Calculate the remaining mass after each half-life: Start with the initial mass of 100.00 mg. After each half-life, the mass is halved.
Use the formula for exponential decay: The remaining mass can be calculated using the formula \( m = m_0 \times \left( \frac{1}{2} \right)^n \), where \( m_0 \) is the initial mass and \( n \) is the number of half-lives.
Substitute the values into the formula: Plug in the initial mass (100.00 mg) and the number of half-lives calculated in step 2 into the formula to find the remaining mass.
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