A sample of radioactive (35)/(16) S disintegrates at a rate of 1.00 ×10^3 atoms min^-1 . The hal

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A sample of radioactive (35)/(16) S disintegrates at a rate...

A sample of radioactive $\frac{35}{16} \mathrm{S}$ disintegrates at a rate of $1.00 \times 10^{3}$ atoms $\min ^{-1} .$ The half-life of $_{16}^{35} \mathrm{S}$ is $87.9 \mathrm{d}$ How long will it take for the activity of this sample to decrease to the point of producing (a) $253 ;$ (b) $104 ;$ and (c) 52 dis $\min ^{-1} ?$

A sample of radioactive $\frac{35}{16} \mathrm{S}$ disintegrates at a rate of $1.00 \times 10^{3}$ atoms $\min ^{-1} .$ The half-life of $_{16}^{35} \mathrm{S}$ is $87.9 \mathrm{d}$
How long will it take for the activity of this sample to decrease to the point of producing (a) $253 ;$ (b) $104 ;$ and (c) 52 dis $\min ^{-1} ?$

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable isotopes lose energy by emitting radiation. This process follows an exponential law, meaning that the number of undecayed nuclei, and thus the activity (rate of decay), decreases exponentially over time.

Activity

Activity refers to the rate at which a radioactive sample undergoes decay, usually measured in disintegrations per minute (or per second). It is directly proportional to the number of radioactive atoms present in the sample and declines exponentially as the atoms decay.

Exponential Decay

Exponential decay is the mathematical model that describes how a quantity diminishes at a rate proportional to its current value. In radioactive decay, this means that the number of undecayed nuclei and the activity decrease exponentially with time.

Half-life

The half-life of a radioactive substance is the time required for half of the nuclei in a sample to decay. It is an intrinsic property of the isotope and is used to calculate other decay parameters, such as the decay constant.

Decay Constant

The decay constant is a parameter that represents the probability per unit time that a given nucleus will decay. It is directly related to the half-life via the formula lambda = ln(2)/half-life and is a key factor in the exponential decay equation for determining the change in activity over time.

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