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The half life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio of 1 : 15 in a sample of agiven rock. The age of the rock was estimatedto be [2011]
- a)150 years
- b)200 years
- c)250 years
- d)100 years
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The half life of a radioactive isotope 'X' is 50 years. It dec...
Let number of atoms in X = Nx
Number of atoms in Y = Ny By question
Number of atoms in Y = Ny By question
∴ Part of Nx 
So, total 4 half lives are passed, so, age of rock is 4 × 50 = 200 years
Most Upvoted Answer
The half life of a radioactive isotope 'X' is 50 years. It dec...
Given: Half life of radioactive isotope X = 50 years
Ratio of X to Y = 1:15 in a rock sample
Let us assume that the initial quantity of X in the rock was 16 units (1+15). After one half-life of X, half of it would have decayed to Y. Therefore, the quantity of X remaining in the rock sample after 50 years would be 8 units, and the quantity of Y formed would be 8 units as well.
Now, let us assume that another 50 years pass (i.e., a total of 100 years). During this time, half of the remaining X atoms (i.e., 4 units) would have decayed to Y, and the quantity of Y formed would be 12 units (8+4). Therefore, the ratio of X to Y after 100 years would be 4:12, which simplifies to 1:3.
It is given that the ratio of X to Y in the rock sample is 1:15. Therefore, we can write:
16 units of X = 1 unit of X + 15 units of Y
After 100 years, we know that 4 units of X and 12 units of Y are present. Substituting these values in the above equation, we get:
4 units of X = 1 unit of X + 3 units of Y
Solving for X, we get:
3 units of X = 3 units of Y
Therefore, the age of the rock sample would be 2 half-lives, or 2 x 50 = 100 years. Hence, the correct option is (b) 200 years.
Ratio of X to Y = 1:15 in a rock sample
Let us assume that the initial quantity of X in the rock was 16 units (1+15). After one half-life of X, half of it would have decayed to Y. Therefore, the quantity of X remaining in the rock sample after 50 years would be 8 units, and the quantity of Y formed would be 8 units as well.
Now, let us assume that another 50 years pass (i.e., a total of 100 years). During this time, half of the remaining X atoms (i.e., 4 units) would have decayed to Y, and the quantity of Y formed would be 12 units (8+4). Therefore, the ratio of X to Y after 100 years would be 4:12, which simplifies to 1:3.
It is given that the ratio of X to Y in the rock sample is 1:15. Therefore, we can write:
16 units of X = 1 unit of X + 15 units of Y
After 100 years, we know that 4 units of X and 12 units of Y are present. Substituting these values in the above equation, we get:
4 units of X = 1 unit of X + 3 units of Y
Solving for X, we get:
3 units of X = 3 units of Y
Therefore, the age of the rock sample would be 2 half-lives, or 2 x 50 = 100 years. Hence, the correct option is (b) 200 years.
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The half life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio of 1 : 15 in a sample of agiven rock. The age of the rock was estimatedto be [2011]a)150 yearsb)200 yearsc)250 yearsd)100 yearsCorrect answer is option 'B'. Can you explain this answer?
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The half life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio of 1 : 15 in a sample of agiven rock. The age of the rock was estimatedto be [2011]a)150 yearsb)200 yearsc)250 yearsd)100 yearsCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The half life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio of 1 : 15 in a sample of agiven rock. The age of the rock was estimatedto be [2011]a)150 yearsb)200 yearsc)250 yearsd)100 yearsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The half life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio of 1 : 15 in a sample of agiven rock. The age of the rock was estimatedto be [2011]a)150 yearsb)200 yearsc)250 yearsd)100 yearsCorrect answer is option 'B'. Can you explain this answer?.
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