The variation of decay rate of two radioactive samples A and...

The variation of decay rate of two radioactive samples $A$ and $B$ with time is shown in figure. (a) Decay constant of $A$ is greater than that of $B$, hence, $A$ always decays faster than $B$. (b) Decay constant of $B$ is greater than that of $A$ but its decay rate is always smaller than that of $A$ (c) Decays constant of $A$ is greater than that of $B$ but it does not always decay faster than $B$ (d) Decay constant of $B$ is smaller than that of $A$ but still its decay rate becomes equal to that of $A$ at a later instant

The variation of decay rate of two radioactive samples $A$ and $B$ with time is shown in figure.
(a) Decay constant of $A$ is greater than that of $B$, hence, $A$ always decays faster than $B$.
(b) Decay constant of $B$ is greater than that of $A$ but its decay rate is always smaller than that of $A$
(c) Decays constant of $A$ is greater than that of $B$ but it does not always decay faster than $B$
(d) Decay constant of $B$ is smaller than that of $A$ but still its decay rate becomes equal to that of $A$ at a later instant

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable nucleus, releasing particles and energy. This stochastic process is characterized by an exponential decrease in the number of undecayed nuclei over time and is governed by the principles of probability and nuclear physics.

Decay Constant

The decay constant, denoted by lambda (?), quantifies the probability per unit time that a nucleus will decay. It is a fundamental parameter in the exponential decay law and directly relates to the rate of decay; a larger decay constant indicates a faster decay process. However, the overall decay behavior also depends on the initial number of radioactive nuclei.

Activity

Activity is the measure of the decay rate of a radioactive sample, typically expressed as the number of decays per unit time. It is directly proportional to both the decay constant and the number of undecayed nuclei present at any given time. This means that even if one sample has a higher decay constant, differences in initial quantities can lead to varying activities over time.

Exponential Decay Law

The exponential decay law mathematically describes how the number of radioactive nuclei decreases over time, following the expression N(t) = N0 * e^(-?t), where N0 is the initial number of nuclei and ? is the decay constant. This law underpins the behavior of radioactive substances and explains how both decay constant and initial amount affect the decay rate observed at any time.

Transcript

Please give Ace some feedback