Use the half-life information to complete each table. (The formula 𝒩=𝒩0 e^k t is not required.)

step 1 So we're given the formula we're supposed to use, but it's not required. We are told the half -l

Use the half-life information to complete each table. (The...

Use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.) (a) Uranium-228: half-life $=550$ seconds$$\begin{array}{llllll}t \text { (seconds) } & 0 & 550 & 1100 & 1650 & 2200 \\\mathcal{N} \text { (grams) } & 8 & & & \\\hline\end{array}$$ (b) Uranium-238: half-life $=4.9 \times 10^{9}$ years$$\begin{array}{lcccccc}\hline \multirow{2}{*}\begin{array}{l}\text { t (years) } \\\mathcal{N} \text { (grams) }\end{array} & \multicolumn{2}{c}0 \\& \multicolumn{2}{c}10 & 5 & 2.5 & 1.25 & 0.625 \\\hline\end{array}$$

Use the half-life information to complete each table. (The formula $\mathcal{N}=\mathcal{N}_{0} e^{k t}$ is not required.)
(a) Uranium-228: half-life $=550$ seconds$$\begin{array}{llllll}t \text { (seconds) } & 0 & 550 & 1100 & 1650 & 2200 \\\mathcal{N} \text { (grams) } & 8 & & & \\\hline\end{array}$$
(b) Uranium-238: half-life $=4.9 \times 10^{9}$ years$$\begin{array}{lcccccc}\hline \multirow{2}{*}\begin{array}{l}\text { t (years) } \\\mathcal{N} \text { (grams) }\end{array} & \multicolumn{2}{c}0 \\& \multicolumn{2}{c}10 & 5 & 2.5 & 1.25 & 0.625 \\\hline\end{array}$$

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Key Concepts

Iterative Halving

Iterative halving is the process of successively applying the half-life concept to determine the remaining quantity after multiple time intervals. Each interval that is equal to one half-life reduces the current quantity by half, allowing for the completion of tables by repeatedly halving the starting amount.

Half-life

The half-life of a radioactive substance is the time required for half of the atoms in a sample to decay. This concept is essential in understanding the rate at which radioactive substances decrease in quantity over time, and it is independent of the initial amount of the substance.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. In the context of radioactive decay, the amount of a substance at any given time can be modeled by an exponential function, even if the formula is not explicitly used, since the underlying principle is that with each half-life the remaining quantity is halved.

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