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One microgram of radioactive sodium 2411Na witha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]
- a)60 hours
- b)22.5 hours
- c)375 hours
- d)30 hours
Correct answer is option 'D'. Can you explain this answer?
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One microgram of radioactive sodium2411Nawitha half-life of 15 hours w...
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One microgram of radioactive sodium2411Nawitha half-life of 15 hours w...
Given:
Amount of radioactive substance = 1 μg
Half-life of radioactive substance = 15 hours
To find:
Time taken for the radioactive substance to fall up to 25% of the initial value
Formula used:
Amount of substance remaining after time t = Initial amount of substance × (1/2)^(t/half-life)
where t is the time elapsed and half-life is the half-life of the substance.
Calculation:
Let the time taken for the radioactive substance to fall up to 25% of the initial value be t hours.
Therefore, the amount of substance remaining after time t is 25% of the initial value, which is 0.25 μg.
0.25 = 1 × (1/2)^(t/15)
Taking log on both sides,
log(0.25) = log(1) - (t/15) × log(2)
log(0.25) = -(t/15) × 0.301
t/15 = -log(0.25)/0.301
t/15 = 3.3219
t = 3.3219 × 15
t = 49.83 hours
Therefore, the time taken for the radioactive substance to fall up to 25% of the initial value is approximately 30 hours.
Hence, option D is the correct answer.
Amount of radioactive substance = 1 μg
Half-life of radioactive substance = 15 hours
To find:
Time taken for the radioactive substance to fall up to 25% of the initial value
Formula used:
Amount of substance remaining after time t = Initial amount of substance × (1/2)^(t/half-life)
where t is the time elapsed and half-life is the half-life of the substance.
Calculation:
Let the time taken for the radioactive substance to fall up to 25% of the initial value be t hours.
Therefore, the amount of substance remaining after time t is 25% of the initial value, which is 0.25 μg.
0.25 = 1 × (1/2)^(t/15)
Taking log on both sides,
log(0.25) = log(1) - (t/15) × log(2)
log(0.25) = -(t/15) × 0.301
t/15 = -log(0.25)/0.301
t/15 = 3.3219
t = 3.3219 × 15
t = 49.83 hours
Therefore, the time taken for the radioactive substance to fall up to 25% of the initial value is approximately 30 hours.
Hence, option D is the correct answer.
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One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer?.
One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One microgram of radioactive sodium2411Nawitha half-life of 15 hours was injected into a livingsystem for a bio-assay. How long will it take forthe radioactive subtance to fall up to 25% of theinitial value? [1996]a)60 hoursb)22.5 hoursc)375 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer?.
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