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Multiple Choice
The isotope Carbon-14 has a half-life of 5,730 years. How many years must pass for a sample of Carbon-14 to break down to ¼ of its original amount? a) 5,730 years b) 17,190 c) 11,460 d) 2,865
A
5,730 years
B
17,190
C
11,460
D
2,865
Verified step by step guidance
1
Understand the concept of half-life: The half-life of an isotope is the time required for half of the isotope to decay. For Carbon-14, this is 5,730 years.
Determine how many half-lives are needed for the sample to reduce to 1/4 of its original amount. Since 1/4 is half of 1/2, it requires two half-lives.
Calculate the total time for two half-lives: Multiply the half-life duration by the number of half-lives needed. Use the formula: \( \text{Total time} = \text{Half-life} \times \text{Number of half-lives} \).
Substitute the values into the formula: \( \text{Total time} = 5,730 \text{ years} \times 2 \).
Interpret the result: The total time calculated will give you the number of years required for the sample to decay to 1/4 of its original amount.