Question

The half-life period of a radioactive element X is same as the mean lifetime 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

Answer 1

Hint: Half-life is the time required for an amount to decrease to half of its underlying worth. The term is normally utilized in atomic material science to depict how rapidly unsteady molecules experience, or how long stable iotas endure, radioactive decay.

Complete step-by-step answer:
The term is additionally utilized all the more for the most part to describe any sort of exponential or non-exponential decay.
The correct answer is C.
\[t_{1/2}^{X}={{t}^{Y}}\]
\[\dfrac{\ln 2}{{{\lambda }_{X}}}=\dfrac{1}{{{\lambda }_{Y}}}\]
Since, \[ln2=0.693 < 1\]
So, \[{{\lambda }_{Y}} > {{\lambda }_{X}}\]

Higher is the decay constant, higher is the rate of decay.
Y decays at the faster rate.

Additional Information:
For instance, the clinical sciences allude to the organic half-life of medications and different synthetic substances in the human body. The opposite of half-life is multiplying time.
Half-life is steady over the lifetime of an exponentially decaying amount, and it is a trademark unit for the exponential decay condition. The going with table shows the decrease of an amount as an element of the quantity of half-lives elapsed.
A half-life as a rule portrays the decay of discrete elements, for example, radioactive iotas. All things considered; it doesn't work to utilize the definition that states "half-life is the time required for precisely half of the substances to decay". For instance, if there is only one radioactive molecule, and its half-life is one second, there won't be "half of an iota" left following one second.
Rather, the half-life is characterized as far as likelihood: "Half-life is the time required for precisely half of the elements to decay by and large". As such, the likelihood of a radioactive particle decaying inside its half-life is 50%.
For instance, the picture on the privilege is a reproduction of numerous indistinguishable molecules experiencing radioactive decay.

Note: After one half-life there are not actually one-half of the iotas staying, just around, as a result of the irregular variety all the while. In any case, when there are numerous indistinguishable molecules decaying (right boxes), the law of huge numbers recommends that it is an excellent estimation to state that half of the iotas stay after one half-life.