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The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then
- a)X and Y have the same decay rate initially
- b)X and Y decay at the same rate always
- c)Y will decay at a faster rate than X
- d)X will decay at a faster rate than Y
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The half life period of a radioactive element X is same as the mean li...
Explanation:
The half-life period of a radioactive element is the time taken for half of the atoms in a sample to decay. The mean life time of a radioactive element is the average time taken for all the atoms in a sample to decay.
Initial Condition:
Initially, both X and Y have the same number of atoms. Let us assume that this number is N.
Decay of X:
After the half-life period, the number of atoms in X will become N/2. This means that the decay rate of X is given by:
R_x = (N - N/2)/T_1/2
where T_1/2 is the half-life period of X.
Simplifying this expression, we get:
R_x = N/(2T_1/2)
Decay of Y:
The mean life time of Y is the same as the half-life period of X. This means that after the half-life period, the number of atoms in Y will also become N/2. However, the decay rate of Y is given by:
R_y = N/T
where T is the mean life time of Y.
Comparing Decay Rates:
To compare the decay rates of X and Y, we need to compare R_x and R_y. Dividing R_y by R_x, we get:
R_y/R_x = (N/T)/(N/(2T_1/2))
Simplifying this expression, we get:
R_y/R_x = 2(T_1/2)/T
Since T is greater than T_1/2, we can conclude that R_y is greater than R_x. This means that Y will decay at a faster rate than X.
Therefore, the correct answer is option C.
The half-life period of a radioactive element is the time taken for half of the atoms in a sample to decay. The mean life time of a radioactive element is the average time taken for all the atoms in a sample to decay.
Initial Condition:
Initially, both X and Y have the same number of atoms. Let us assume that this number is N.
Decay of X:
After the half-life period, the number of atoms in X will become N/2. This means that the decay rate of X is given by:
R_x = (N - N/2)/T_1/2
where T_1/2 is the half-life period of X.
Simplifying this expression, we get:
R_x = N/(2T_1/2)
Decay of Y:
The mean life time of Y is the same as the half-life period of X. This means that after the half-life period, the number of atoms in Y will also become N/2. However, the decay rate of Y is given by:
R_y = N/T
where T is the mean life time of Y.
Comparing Decay Rates:
To compare the decay rates of X and Y, we need to compare R_x and R_y. Dividing R_y by R_x, we get:
R_y/R_x = (N/T)/(N/(2T_1/2))
Simplifying this expression, we get:
R_y/R_x = 2(T_1/2)/T
Since T is greater than T_1/2, we can conclude that R_y is greater than R_x. This means that Y will decay at a faster rate than X.
Therefore, the correct answer is option C.
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The half life period of a radioactive element X is same as the mean li...
Half life is less than mean life for any element. therefore half life of y is less than its mean life that means it is also less than the half life of X. So Y will decay at a faster rate than X.
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The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect answer is option 'C'. Can you explain this answer?
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The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect 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 The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect 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 The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect answer is option 'C'. Can you explain this answer?.
The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect 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 The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect 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 The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Thena)X and Y have the same decay rate initiallyb)X and Y decay at the same rate alwaysc)Y will decay at a faster rate than Xd)X will decay at a faster rate than YCorrect answer is option 'C'. Can you explain this answer?.
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