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An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?
- a)64
- b)90
- c)108
- d)120
Correct answer is option 'C'. Can you explain this answer?
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An accident in a nuclear labora tory resulted in deposition of a certa...
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To find the minimum number of days after which the laboratory can be considered safe for use, we need to determine the time it takes for the radioactive material to decay to a level that is permissible for safe operation.
Let's assume the initial amount of radioactive material is 'A' and the permissible level is 'P'. It is given that the radiation is 64 times more than the permissible level, so we can write:
A/P = 64
The half-life of the radioactive material is given as 18 days. This means that after every 18 days, the amount of radioactive material is reduced to half.
Now, let's consider the radioactive material after 'n' half-lives. The amount of radioactive material remaining after 'n' half-lives can be given as:
A * (1/2)^n
We want to find the minimum number of days, 'D', after which the radiation is reduced to the permissible level. So, we can write:
A * (1/2)^D = P
Now, substituting the value of A/P from the first equation, we get:
64 * (1/2)^D = 1
Simplifying the equation, we have:
2^6 * (1/2)^D = 1
2^(6-D) = 1
The only possible value of D that satisfies the equation is 6. Therefore, the minimum number of days after which the laboratory can be considered safe for use is 6 * 18 = 108 days.
So, the correct answer is option 'C' - 108 days.
Let's assume the initial amount of radioactive material is 'A' and the permissible level is 'P'. It is given that the radiation is 64 times more than the permissible level, so we can write:
A/P = 64
The half-life of the radioactive material is given as 18 days. This means that after every 18 days, the amount of radioactive material is reduced to half.
Now, let's consider the radioactive material after 'n' half-lives. The amount of radioactive material remaining after 'n' half-lives can be given as:
A * (1/2)^n
We want to find the minimum number of days, 'D', after which the radiation is reduced to the permissible level. So, we can write:
A * (1/2)^D = P
Now, substituting the value of A/P from the first equation, we get:
64 * (1/2)^D = 1
Simplifying the equation, we have:
2^6 * (1/2)^D = 1
2^(6-D) = 1
The only possible value of D that satisfies the equation is 6. Therefore, the minimum number of days after which the laboratory can be considered safe for use is 6 * 18 = 108 days.
So, the correct answer is option 'C' - 108 days.
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An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer?
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An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer?.
An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?a)64b)90c)108d)120Correct answer is option 'C'. Can you explain this answer?.
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