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For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:
- a)20
- b)10
- c)30
- d)15
Correct answer is option 'A'. Can you explain this answer?
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For a radioactive material, half-life is 10 minutes. If initially ther...
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For a radioactive material, half-life is 10 minutes. If initially ther...
Solution:
Given:
Half-life of radioactive material = 10 minutes
Initial number of nuclei = 600
We know that in a radioactive material, the number of nuclei decreases exponentially with time. The formula for the number of nuclei present at any time t is given by:
N = N0/2^(t/T)
Where
N0 = initial number of nuclei
N = number of nuclei remaining after time t
T = half-life of the substance
Now, we need to find the time taken for the disintegration of 450 nuclei. Let's plug in the values in the above equation:
450 = 600/2^(t/10)
2^(t/10) = 4/3
Taking logarithm on both sides, we get:
t/10 = log2(4/3)
t = 10 log2(4/3)
t ≈ 19.09 minutes
Therefore, the time taken for the disintegration of 450 nuclei is approximately 19.09 minutes.
Answer:
The correct option is A) 20 minutes.
Given:
Half-life of radioactive material = 10 minutes
Initial number of nuclei = 600
We know that in a radioactive material, the number of nuclei decreases exponentially with time. The formula for the number of nuclei present at any time t is given by:
N = N0/2^(t/T)
Where
N0 = initial number of nuclei
N = number of nuclei remaining after time t
T = half-life of the substance
Now, we need to find the time taken for the disintegration of 450 nuclei. Let's plug in the values in the above equation:
450 = 600/2^(t/10)
2^(t/10) = 4/3
Taking logarithm on both sides, we get:
t/10 = log2(4/3)
t = 10 log2(4/3)
t ≈ 19.09 minutes
Therefore, the time taken for the disintegration of 450 nuclei is approximately 19.09 minutes.
Answer:
The correct option is A) 20 minutes.
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For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:a)20b)10c)30d)15Correct answer is option 'A'. Can you explain this answer?
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