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Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x?
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Radioactive nuclei P and Q disintegrate into R with half lives 1 month...
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Radioactive nuclei P and Q disintegrate into R with half lives 1 month...
Given information:
- Radioactive nuclei P and Q disintegrate into R.
- The half-life of P is 1 month.
- The half-life of Q is 2 months.
- At time t=0, the number of nuclei of P and Q is x.
To find:
- The time at which the rate of disintegration of P and Q are equal.
- The number of nuclei of R at that time.
Solution:
Let's assume that after time t, the number of nuclei of P remaining is x/2^n, and the number of nuclei of Q remaining is x/2^m. Here, n and m represents the number of half-lives for P and Q respectively.
Rate of disintegration of P and Q:
The rate of disintegration of a radioactive nucleus is given by the equation:
Rate = (Number of nuclei remaining)/(Half-life)
Therefore, the rate of disintegration of P is x/2^n * 1/t_1, where t_1 is the half-life of P (1 month).
Similarly, the rate of disintegration of Q is x/2^m * 1/t_2, where t_2 is the half-life of Q (2 months).
Setting up the equation:
At the time when the rate of disintegration of P and Q are equal, we have:
x/2^n * 1/t_1 = x/2^m * 1/t_2
Simplifying this equation, we get:
2^m * t_2 = 2^n * t_1
Finding the value of m:
Since the half-life of Q is 2 months, we can say that after 2 months, the number of nuclei of Q remaining is x/2^1 = x/2.
Therefore, m = 1.
Finding the value of n:
To find the value of n, we can make use of the fact that the half-life of P is 1 month.
After 1 month, the number of nuclei of P remaining is x/2^1 = x/2.
Therefore, n = 1.
Calculating the number of nuclei of R:
After time t, the number of nuclei of R is given by the sum of the remaining nuclei of P and Q. So, the number of nuclei of R is:
x/2^n + x/2^m = x/2^1 + x/2^1 = 2x/2 = x
Therefore, the number of nuclei of R is x.
Final answer:
- The time at which the rate of disintegration of P and Q are equal is when n = 1 and m = 1.
- The number of nuclei of R at that time is x.
Conclusion:
At the time when the rate of disintegration of P and Q are equal, the number of nuclei of R is x. Therefore, the correct answer is (1) x.
- Radioactive nuclei P and Q disintegrate into R.
- The half-life of P is 1 month.
- The half-life of Q is 2 months.
- At time t=0, the number of nuclei of P and Q is x.
To find:
- The time at which the rate of disintegration of P and Q are equal.
- The number of nuclei of R at that time.
Solution:
Let's assume that after time t, the number of nuclei of P remaining is x/2^n, and the number of nuclei of Q remaining is x/2^m. Here, n and m represents the number of half-lives for P and Q respectively.
Rate of disintegration of P and Q:
The rate of disintegration of a radioactive nucleus is given by the equation:
Rate = (Number of nuclei remaining)/(Half-life)
Therefore, the rate of disintegration of P is x/2^n * 1/t_1, where t_1 is the half-life of P (1 month).
Similarly, the rate of disintegration of Q is x/2^m * 1/t_2, where t_2 is the half-life of Q (2 months).
Setting up the equation:
At the time when the rate of disintegration of P and Q are equal, we have:
x/2^n * 1/t_1 = x/2^m * 1/t_2
Simplifying this equation, we get:
2^m * t_2 = 2^n * t_1
Finding the value of m:
Since the half-life of Q is 2 months, we can say that after 2 months, the number of nuclei of Q remaining is x/2^1 = x/2.
Therefore, m = 1.
Finding the value of n:
To find the value of n, we can make use of the fact that the half-life of P is 1 month.
After 1 month, the number of nuclei of P remaining is x/2^1 = x/2.
Therefore, n = 1.
Calculating the number of nuclei of R:
After time t, the number of nuclei of R is given by the sum of the remaining nuclei of P and Q. So, the number of nuclei of R is:
x/2^n + x/2^m = x/2^1 + x/2^1 = 2x/2 = x
Therefore, the number of nuclei of R is x.
Final answer:
- The time at which the rate of disintegration of P and Q are equal is when n = 1 and m = 1.
- The number of nuclei of R at that time is x.
Conclusion:
At the time when the rate of disintegration of P and Q are equal, the number of nuclei of R is x. Therefore, the correct answer is (1) x.
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Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x?
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Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x?.
Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x?.
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Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x?, a detailed solution for Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? has been provided alongside types of Radioactive nuclei P and Q disintegrate into R with half lives 1 month and 2 months respectively. At time t =0, number of nuclei of each P and Q is x. Time at which rate of disintegration of P and Q are equal, numberof nuclei of R is (1)x (2)1.25 x (3)1.5 x (4)1.75 x? theory, EduRev gives you an
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