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The half life period of a radioactive material is 15 minutes. What percent of radioactivity of that material will remain after 45 minutes?
- a)10%
- b)12.5%
- c)15%
- d)17.5%
Correct answer is option 'B'. Can you explain this answer?
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The half life period of a radioactive material is 15 minutes. What per...
Solution:
Given,
Half-life period of radioactive material = 15 minutes
Time elapsed = 45 minutes
Let N be the initial number of radioactive atoms.
After one half-life period, the number of radioactive atoms remaining will be N/2.
After two half-life periods, the number of radioactive atoms remaining will be (N/2)/2 = N/4.
After three half-life periods, the number of radioactive atoms remaining will be (N/4)/2 = N/8.
Thus, the fraction of radioactive atoms remaining after n half-life periods is (1/2)^n.
Now, we need to find the fraction of radioactive atoms remaining after 45 minutes, which is 3 half-life periods.
Fraction of radioactive atoms remaining = (1/2)^3 = 1/8
Percent of radioactivity remaining = (1/8) * 100% = 12.5%
Therefore, option (B) is the correct answer.
Given,
Half-life period of radioactive material = 15 minutes
Time elapsed = 45 minutes
Let N be the initial number of radioactive atoms.
After one half-life period, the number of radioactive atoms remaining will be N/2.
After two half-life periods, the number of radioactive atoms remaining will be (N/2)/2 = N/4.
After three half-life periods, the number of radioactive atoms remaining will be (N/4)/2 = N/8.
Thus, the fraction of radioactive atoms remaining after n half-life periods is (1/2)^n.
Now, we need to find the fraction of radioactive atoms remaining after 45 minutes, which is 3 half-life periods.
Fraction of radioactive atoms remaining = (1/2)^3 = 1/8
Percent of radioactivity remaining = (1/8) * 100% = 12.5%
Therefore, option (B) is the correct answer.
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The half life period of a radioactive material is 15 minutes. What percent of radioactivity of that material will remain after 45 minutes?a)10%b)12.5%c)15%d)17.5%Correct answer is option 'B'. Can you explain this answer?
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