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A radioactive element X converts into another stable element Y. Half life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1 : 4, then t in hours is
- a)2
- b)4
- c)between 4 and 6
- d)6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A radioactive element X converts into another stable element Y. Half l...
Let N0 be the number of atoms of X at time t = 0.
Then at t = 4 hrs (two half lives)
∴ Nx/Ny = 1/3
and at t = 6 hrs (three half lives)
The given ratio 1/4 lies between 1/3 and 1/7.
Therefore, t lies between 4 hrs and 6 hrs.
Then at t = 4 hrs (two half lives)
∴ Nx/Ny = 1/3
and at t = 6 hrs (three half lives)
The given ratio 1/4 lies between 1/3 and 1/7.
Therefore, t lies between 4 hrs and 6 hrs.
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A radioactive element X converts into another stable element Y. Half l...
Answer:
To solve this problem, we need to understand the concept of half-life and radioactive decay.
Understanding Half-life:
The half-life of a radioactive element is the time it takes for half of the atoms of that element to decay. In this case, the half-life of element X is given as 2 hours. This means that after every 2 hours, half of the atoms of element X will decay and convert into element Y.
Initial Condition:
At the beginning, only element X is present. Let's assume that there are 'n' atoms of element X.
After time t:
After time t, the ratio of atoms of X and Y is found to be 1:4. This means that there are 'n/5' atoms of element X and '4n/5' atoms of element Y.
Calculating the time t:
To calculate the time t, we need to find the number of half-lives that have occurred. Since each half-life is 2 hours, the total time t can be calculated as:
t = number of half-lives x half-life period
t = (n/5) / n x 2
t = 2/5 hours
Therefore, the time t is between 4 and 6 hours, which corresponds to option C.
To solve this problem, we need to understand the concept of half-life and radioactive decay.
Understanding Half-life:
The half-life of a radioactive element is the time it takes for half of the atoms of that element to decay. In this case, the half-life of element X is given as 2 hours. This means that after every 2 hours, half of the atoms of element X will decay and convert into element Y.
Initial Condition:
At the beginning, only element X is present. Let's assume that there are 'n' atoms of element X.
After time t:
After time t, the ratio of atoms of X and Y is found to be 1:4. This means that there are 'n/5' atoms of element X and '4n/5' atoms of element Y.
Calculating the time t:
To calculate the time t, we need to find the number of half-lives that have occurred. Since each half-life is 2 hours, the total time t can be calculated as:
t = number of half-lives x half-life period
t = (n/5) / n x 2
t = 2/5 hours
Therefore, the time t is between 4 and 6 hours, which corresponds to option C.
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A radioactive element X converts into another stable element Y. Half life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1 : 4, then t in hours isa)2b)4c)between 4 and 6d)6Correct answer is option 'C'. Can you explain this answer?
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