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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?
(AIEEE 2007)
- a)1000 days
- b)300 days
- c)10 days
- d)100 days
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A radioactive element gets spilled over the floor of a room. Its half-...
Taking log on both sides
log 10 = n log 2
Time = n x half-life = 3.32 x 30
= 99.6 days
= 100 days
Most Upvoted Answer
A radioactive element gets spilled over the floor of a room. Its half-...
Given:
- Half-life period of the radioactive element = 30 days
- Initial activity = 10 times the permissible value
To Find:
After how many days will it be safe to enter the room?
Solution:
To determine when it will be safe to enter the room, we need to find the time it takes for the activity of the radioactive element to decrease to the permissible value.
1. Initial Activity:
Let's assume the initial activity of the radioactive element is A₀.
2. Half-life:
The half-life period of the radioactive element is given as 30 days. This means that after every 30 days, the activity of the element will reduce to half of its initial value.
3. Activity after one half-life:
After the first half-life, the activity will be reduced to A₀/2.
4. Activity after two half-lives:
After the second half-life, the activity will be further reduced to (A₀/2)/2 = A₀/4.
5. Activity after three half-lives:
After the third half-life, the activity will be reduced to ((A₀/2)/2)/2 = A₀/8.
6. Activity after n half-lives:
The activity of the radioactive element after n half-lives can be calculated using the formula:
Aₙ = A₀/(2^n)
7. Permissible Value:
The permissible value of the activity is given as A₀/10.
8. Solving for n:
To find the number of half-lives it takes for the activity to reduce to the permissible value, we can set the activity after n half-lives equal to the permissible value and solve for n:
A₀/(2^n) = A₀/10
9. Simplifying the equation:
Dividing both sides of the equation by A₀ gives:
1/(2^n) = 1/10
Taking the reciprocal of both sides gives:
2^n = 10
10. Solving for n:
Taking the logarithm of both sides (with base 2) gives:
n = log₂(10)
Using a calculator, we find that n ≈ 3.32.
Since n represents the number of half-lives, we round up to the nearest whole number. Therefore, it will take 4 half-lives for the activity to reduce to the permissible value.
11. Time it takes for 4 half-lives:
Since the half-life period of the radioactive element is 30 days, the time it takes for 4 half-lives is:
4 x 30 = 120 days
Therefore, it will be safe to enter the room after 120 days, which is approximately 100 days (option D).
- Half-life period of the radioactive element = 30 days
- Initial activity = 10 times the permissible value
To Find:
After how many days will it be safe to enter the room?
Solution:
To determine when it will be safe to enter the room, we need to find the time it takes for the activity of the radioactive element to decrease to the permissible value.
1. Initial Activity:
Let's assume the initial activity of the radioactive element is A₀.
2. Half-life:
The half-life period of the radioactive element is given as 30 days. This means that after every 30 days, the activity of the element will reduce to half of its initial value.
3. Activity after one half-life:
After the first half-life, the activity will be reduced to A₀/2.
4. Activity after two half-lives:
After the second half-life, the activity will be further reduced to (A₀/2)/2 = A₀/4.
5. Activity after three half-lives:
After the third half-life, the activity will be reduced to ((A₀/2)/2)/2 = A₀/8.
6. Activity after n half-lives:
The activity of the radioactive element after n half-lives can be calculated using the formula:
Aₙ = A₀/(2^n)
7. Permissible Value:
The permissible value of the activity is given as A₀/10.
8. Solving for n:
To find the number of half-lives it takes for the activity to reduce to the permissible value, we can set the activity after n half-lives equal to the permissible value and solve for n:
A₀/(2^n) = A₀/10
9. Simplifying the equation:
Dividing both sides of the equation by A₀ gives:
1/(2^n) = 1/10
Taking the reciprocal of both sides gives:
2^n = 10
10. Solving for n:
Taking the logarithm of both sides (with base 2) gives:
n = log₂(10)
Using a calculator, we find that n ≈ 3.32.
Since n represents the number of half-lives, we round up to the nearest whole number. Therefore, it will take 4 half-lives for the activity to reduce to the permissible value.
11. Time it takes for 4 half-lives:
Since the half-life period of the radioactive element is 30 days, the time it takes for 4 half-lives is:
4 x 30 = 120 days
Therefore, it will be safe to enter the room after 120 days, which is approximately 100 days (option D).
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Community Answer
A radioactive element gets spilled over the floor of a room. Its half-...
Taking log on both sides
log 10 = n log 2
Time = n x half-life = 3.32 x 30
= 99.6 days
= 100 days
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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer?
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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer?.
A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?(AIEEE 2007)a)1000 daysb)300 daysc)10 daysd)100 daysCorrect answer is option 'D'. Can you explain this answer?.
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