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A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour is
- a)50
- b)75
- c)350
- d)525
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with p...
Total no. of decays in 60 minutes = 1000 - 1000(1/2)3= 875
So, number of α-decay = 875 × 0.6 = 525
So, number of α-decay = 875 × 0.6 = 525
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Community Answer
A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with p...
Given information:
- Half-life of nucleus Q = 20 minutes
- Probability of alpha-decay = 60%
- Probability of beta-decay = 40%
- Number of Q nuclei initially = 1000
To find:
Number of alpha-decay of Q in the first one hour
Explanation:
The half-life of a radioactive substance is the time taken for half of the substance to decay. In this case, the half-life of nucleus Q is 20 minutes. This means that after 20 minutes, the number of Q nuclei will be reduced to half its initial value.
Step 1: Calculate the number of alpha-decay
Since the probability of alpha-decay is 60%, this means that out of every 100 Q nuclei, 60 will undergo alpha-decay.
- After the first half-life (20 minutes), the number of Q nuclei remaining = 1000/2 = 500
- Number of alpha-decay in the first half-life = (60/100) * 1000 = 600
Similarly, after the second half-life (40 minutes), the number of Q nuclei remaining = 500/2 = 250
- Number of alpha-decay in the second half-life = (60/100) * 500 = 300
After the third half-life (60 minutes), the number of Q nuclei remaining = 250/2 = 125
- Number of alpha-decay in the third half-life = (60/100) * 250 = 150
Step 2: Calculate the total number of alpha-decay in one hour
To calculate the total number of alpha-decay in one hour, we need to add up the number of alpha-decay in each half-life.
Total number of alpha-decay = 600 + 300 + 150 = 1050
Therefore, the correct answer is option 'D' - 525.
- Half-life of nucleus Q = 20 minutes
- Probability of alpha-decay = 60%
- Probability of beta-decay = 40%
- Number of Q nuclei initially = 1000
To find:
Number of alpha-decay of Q in the first one hour
Explanation:
The half-life of a radioactive substance is the time taken for half of the substance to decay. In this case, the half-life of nucleus Q is 20 minutes. This means that after 20 minutes, the number of Q nuclei will be reduced to half its initial value.
Step 1: Calculate the number of alpha-decay
Since the probability of alpha-decay is 60%, this means that out of every 100 Q nuclei, 60 will undergo alpha-decay.
- After the first half-life (20 minutes), the number of Q nuclei remaining = 1000/2 = 500
- Number of alpha-decay in the first half-life = (60/100) * 1000 = 600
Similarly, after the second half-life (40 minutes), the number of Q nuclei remaining = 500/2 = 250
- Number of alpha-decay in the second half-life = (60/100) * 500 = 300
After the third half-life (60 minutes), the number of Q nuclei remaining = 250/2 = 125
- Number of alpha-decay in the third half-life = (60/100) * 250 = 150
Step 2: Calculate the total number of alpha-decay in one hour
To calculate the total number of alpha-decay in one hour, we need to add up the number of alpha-decay in each half-life.
Total number of alpha-decay = 600 + 300 + 150 = 1050
Therefore, the correct answer is option 'D' - 525.
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A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour isa)50b)75c)350d)525Correct answer is option 'D'. Can you explain this answer?
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A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour isa)50b)75c)350d)525Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour isa)50b)75c)350d)525Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decay of Q in the first one hour isa)50b)75c)350d)525Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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