You have two piles of different unknown radioactive...

You have two piles of different unknown radioactive substances: pile $A$ with a mass of $200 \mathrm{~g}$, and pile $\mathrm{B}$ with a mass of $100 \mathrm{~g} .$ Would it be possible for these two piles to have the same rate of radioactive decay? Explain.

Key Concepts

Radioactive Decay

Radioactive decay is a random process by which unstable atomic nuclei emit particles or energy to reach a more stable state. It is characterized by the fact that the decay events are random at the level of individual atoms, but predictable statistically for a large number of atoms.

Activity

Activity is the measure of the number of decay events per unit time in a radioactive material, often expressed in becquerels or curies. It depends on both the amount (or mass) of the substance and its intrinsic decay properties, meaning that two samples can exhibit the same activity if differences in mass are compensated by differences in decay rates.

Decay Constant

The decay constant is a specific property of a radioactive substance that indicates the probability of decay of a nucleus per unit time. It directly influences the decay rate, such that a higher decay constant results in a higher probability of decay. Even with different masses, substances with appropriately differing decay constants can have equivalent rates of decay.

Relationship Between Mass and Radioactivity

The mass of a radioactive substance is related to the number of radioactive atoms present, but the overall activity also depends on the particular decay constant of the substance. Therefore, it is theoretically possible for two piles with different masses to exhibit the same radioactive decay rate if the substance with the lesser mass has a higher decay constant or specific activity.

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