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The half life of a radioactive isotope X is 50 years. It decays to another element Y
which is stable. The two elements X and Y were found to be in the ratio of 1: 15 in a
sample of a given rock. The age of the rock was estimated to be
which is stable. The two elements X and Y were found to be in the ratio of 1: 15 in a
sample of a given rock. The age of the rock was estimated to be
- a)100 years
- b)150 years
- c)200 years
- d)250 years
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The half life of a radioactive isotope X is 50 years. It decays to ano...
After t second fractional amount of X left is 
t = 4 × T1/2
t = 4 × 50
= 200 years
t = 4 × 50
= 200 years
Most Upvoted Answer
The half life of a radioactive isotope X is 50 years. It decays to ano...
X:y=1:15
initial value of X=N0
after decay the amount of X remain=No/16N=No(1/2)*t/T
No/16/No=(1/2)*t/50
1/16=(1/2)*t/50=(1/2)*4=(1/2)*t/50
4=t/50
t=200years
initial value of X=N0
after decay the amount of X remain=No/16N=No(1/2)*t/T
No/16/No=(1/2)*t/50
1/16=(1/2)*t/50=(1/2)*4=(1/2)*t/50
4=t/50
t=200years
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Community Answer
The half life of a radioactive isotope X is 50 years. It decays to ano...
The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. In this case, the half-life of isotope X is given as 50 years. This means that after 50 years, half of the isotope X will have decayed to form the stable element Y.
To determine the age of the rock, we can use the ratio of X to Y in the sample. The ratio is given as 1:15, which means that for every 1 unit of X, there are 15 units of Y.
Let's assume that the initial amount of X in the rock sample is 1 unit. After 50 years, half of this amount will have decayed, leaving 0.5 units of X. At the same time, Y would have been formed, so the total amount of Y in the sample would be 15 units.
After another 50 years (totaling 100 years), half of the remaining X will decay. This means that 0.25 units of X will be left. At the same time, the amount of Y will increase to 30 units.
We can continue this process, halving the amount of X every 50 years and doubling the amount of Y. After 150 years, there will be 0.125 units of X and 60 units of Y.
After 200 years, there will be 0.0625 units of X and 120 units of Y.
Finally, after 250 years, there will be 0.03125 units of X and 240 units of Y.
At this point, the ratio of X to Y is approximately 1:15, which matches the given ratio in the rock sample. Therefore, the age of the rock is estimated to be 200 years.
So, the correct answer is option C) 200 years.
To determine the age of the rock, we can use the ratio of X to Y in the sample. The ratio is given as 1:15, which means that for every 1 unit of X, there are 15 units of Y.
Let's assume that the initial amount of X in the rock sample is 1 unit. After 50 years, half of this amount will have decayed, leaving 0.5 units of X. At the same time, Y would have been formed, so the total amount of Y in the sample would be 15 units.
After another 50 years (totaling 100 years), half of the remaining X will decay. This means that 0.25 units of X will be left. At the same time, the amount of Y will increase to 30 units.
We can continue this process, halving the amount of X every 50 years and doubling the amount of Y. After 150 years, there will be 0.125 units of X and 60 units of Y.
After 200 years, there will be 0.0625 units of X and 120 units of Y.
Finally, after 250 years, there will be 0.03125 units of X and 240 units of Y.
At this point, the ratio of X to Y is approximately 1:15, which matches the given ratio in the rock sample. Therefore, the age of the rock is estimated to be 200 years.
So, the correct answer is option C) 200 years.
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The half life of a radioactive isotope X is 50 years. It decays to another element Ywhich is stable. The two elements X and Y were found to be in the ratio of 1: 15 in asample of a given rock. The age of the rock was estimated to bea)100 yearsb)150 yearsc)200 yearsd)250 yearsCorrect answer is option 'C'. Can you explain this answer?
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