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A radioactive element has a half life of 15 years. The fraction that will decay in 30 years is
- a)3/4
- b)1/4
- c)2/3
- d)1/3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A radioactive element has a half life of 15 years. The fraction that w...
Explanation:
Half-Life Concept:
- The half-life of a radioactive element is the time it takes for half of the original amount of the element to decay.
- In this case, the half-life of the radioactive element is 15 years.
Fraction Decay in 30 years:
- Since the half-life of the element is 15 years, after 30 years, two half-lives have passed.
- After the first half-life (15 years), half of the element would have decayed.
- After the second half-life (another 15 years), half of the remaining half would have decayed.
Calculation:
- After 30 years, 1/2 of the original amount decays after the first half-life.
- After the second half-life, 1/2 of the remaining 1/2 decays.
- Therefore, the fraction that will decay in 30 years is 1/2 + 1/2 * 1/2 = 3/4.
Therefore, the correct answer is option 'A' (3/4).
Half-Life Concept:
- The half-life of a radioactive element is the time it takes for half of the original amount of the element to decay.
- In this case, the half-life of the radioactive element is 15 years.
Fraction Decay in 30 years:
- Since the half-life of the element is 15 years, after 30 years, two half-lives have passed.
- After the first half-life (15 years), half of the element would have decayed.
- After the second half-life (another 15 years), half of the remaining half would have decayed.
Calculation:
- After 30 years, 1/2 of the original amount decays after the first half-life.
- After the second half-life, 1/2 of the remaining 1/2 decays.
- Therefore, the fraction that will decay in 30 years is 1/2 + 1/2 * 1/2 = 3/4.
Therefore, the correct answer is option 'A' (3/4).
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