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A radioactive material (t1/2 = 30 days) gets spilled over the floor of a room. If initial activity is ten times the permissible value, after how many days will it be safe to enter the room
- a)100
- b)1000
- c)300
- d)10
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A radioactive material (t1/2= 30 days) gets spilled over the floor of ...
It will be safe to enter the room after the nuclei decreases to 1/10 of its initial amount.
→ Half life = 30 days
→ Using integration law,
∴ After 100 days, it will be safe to enter the room.
Most Upvoted Answer
A radioactive material (t1/2= 30 days) gets spilled over the floor of ...
Given:
- Half-life of the radioactive material = 30 days
- Initial activity = 10 times the permissible value
To find:
After how many days will it be safe to enter the room?
Solution:
The half-life of a radioactive material is the time taken for the activity (or the amount) of the material to reduce to half of its initial value.
Step 1: Calculate the permissible value
Since the initial activity is 10 times the permissible value, we need to find the permissible value first. Let's assume the permissible value is 'P'.
According to the given information, the initial activity = 10 * P
Step 2: Calculate the number of half-lives required
To find the number of half-lives required for the activity to reduce to the permissible value, we can use the formula:
Number of half-lives = log(initial activity / permissible value) / log(2)
Number of half-lives = log(10 * P / P) / log(2) = log(10) / log(2) = 3.32 (approximately)
Since the number of half-lives is always rounded up to the nearest whole number, we need 4 half-lives for the activity to reduce to the permissible value.
Step 3: Calculate the time required
Since the half-life of the radioactive material is 30 days, the time required for one half-life is 30 days.
Therefore, the time required for 4 half-lives = 4 * 30 = 120 days.
Hence, it will be safe to enter the room after 120 days.
Conclusion:
After 120 days, it will be safe to enter the room.
- Half-life of the radioactive material = 30 days
- Initial activity = 10 times the permissible value
To find:
After how many days will it be safe to enter the room?
Solution:
The half-life of a radioactive material is the time taken for the activity (or the amount) of the material to reduce to half of its initial value.
Step 1: Calculate the permissible value
Since the initial activity is 10 times the permissible value, we need to find the permissible value first. Let's assume the permissible value is 'P'.
According to the given information, the initial activity = 10 * P
Step 2: Calculate the number of half-lives required
To find the number of half-lives required for the activity to reduce to the permissible value, we can use the formula:
Number of half-lives = log(initial activity / permissible value) / log(2)
Number of half-lives = log(10 * P / P) / log(2) = log(10) / log(2) = 3.32 (approximately)
Since the number of half-lives is always rounded up to the nearest whole number, we need 4 half-lives for the activity to reduce to the permissible value.
Step 3: Calculate the time required
Since the half-life of the radioactive material is 30 days, the time required for one half-life is 30 days.
Therefore, the time required for 4 half-lives = 4 * 30 = 120 days.
Hence, it will be safe to enter the room after 120 days.
Conclusion:
After 120 days, it will be safe to enter the room.
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A radioactive material (t1/2= 30 days) gets spilled over the floor of a room. If initial activity is ten times the permissible value, after how many days will it be safe to enter the rooma)100b)1000c)300d)10Correct answer is option 'A'. Can you explain this answer?
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