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The half-life period of a radioactive element X is the same as the mean life time of another radioactive element Y. Initially, they have the same number of atoms. Then,
- a)X and Y will always decay at the same rate
- b)Y will decay faster than X
- c)X will decay faster than Y
- d)X and Y will have the same decay rate initially
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The half-life period of a radioactive element X is the same as the me...
Explanation:
Radioactive decay is a random process that occurs in unstable atomic nuclei. The rate of decay of a radioactive element is determined by its half-life or mean life time.
Half-life:
The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. It is a measure of the stability of the element. For example, if the half-life of element X is 1 hour, it means that after 1 hour, half of the atoms in the sample will have decayed.
Mean life time:
The mean life time of a radioactive element is the average time it takes for an atom to decay. It is calculated by taking the reciprocal of the decay constant. The decay constant is a measure of the probability of decay per unit time. If the mean life time of element Y is 1 hour, it means that on average, an atom of Y will decay after 1 hour.
Comparison between X and Y:
Given that the half-life of X is the same as the mean life time of Y, it means that X and Y have the same decay constant. This implies that the probability of decay per unit time is the same for both X and Y.
Decay rate:
The decay rate is the number of decays per unit time. It is given by the equation: decay rate = decay constant * number of atoms.
Explanation of options:
a) X and Y will always decay at the same rate: This is not true because the decay rate depends on the number of atoms, which can vary for X and Y.
b) Y will decay faster than X: This is the correct option. Since X and Y have the same decay constant, the decay rate of Y will be higher than X if they initially have the same number of atoms.
c) X will decay faster than Y: This is not true because X and Y have the same decay constant.
d) X and Y will have the same decay rate initially: This is not true because the decay rate depends on the number of atoms, which can vary for X and Y.
Radioactive decay is a random process that occurs in unstable atomic nuclei. The rate of decay of a radioactive element is determined by its half-life or mean life time.
Half-life:
The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. It is a measure of the stability of the element. For example, if the half-life of element X is 1 hour, it means that after 1 hour, half of the atoms in the sample will have decayed.
Mean life time:
The mean life time of a radioactive element is the average time it takes for an atom to decay. It is calculated by taking the reciprocal of the decay constant. The decay constant is a measure of the probability of decay per unit time. If the mean life time of element Y is 1 hour, it means that on average, an atom of Y will decay after 1 hour.
Comparison between X and Y:
Given that the half-life of X is the same as the mean life time of Y, it means that X and Y have the same decay constant. This implies that the probability of decay per unit time is the same for both X and Y.
Decay rate:
The decay rate is the number of decays per unit time. It is given by the equation: decay rate = decay constant * number of atoms.
Explanation of options:
a) X and Y will always decay at the same rate: This is not true because the decay rate depends on the number of atoms, which can vary for X and Y.
b) Y will decay faster than X: This is the correct option. Since X and Y have the same decay constant, the decay rate of Y will be higher than X if they initially have the same number of atoms.
c) X will decay faster than Y: This is not true because X and Y have the same decay constant.
d) X and Y will have the same decay rate initially: This is not true because the decay rate depends on the number of atoms, which can vary for X and Y.
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The half-life period of a radioactive element X is the same as the me...
T1/2 (half life of X) = τY (mean life of Y)
⇒ λx = λY(0.693)
Y will decay faster than X.
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The half-life period of a radioactive element X is the same as the mean life time of another radioactive element Y. Initially, they have the same number of atoms. Then,a)X and Y will always decay at the same rateb)Y will decay faster than Xc)X will decay faster than Yd)X and Y will have the same decay rate initiallyCorrect answer is option 'B'. Can you explain this answer?
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