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Chapter 18: Problem 59

The half-life of an element \(X\) is 5.25 y. How many days are required for one-fourth of a given amount of \(X\) to decay?

Short Answer

Expert verified
It would take approximately 3835 days for one-fourth of the element X to decay.

Step by step solution

01

Understanding Half-life

The amount of a radioactive substance decreases to half its original amount in one half-life. To figure out how long it takes for one-fourth of a sample to remain, we have to remember that this occurrence would require two 'half-lives'. This is because half of the half (or one fourth) would be remaining after two half-lives.
02

Convert Half-Life from Years to Days

To apply any time-related calculations, we need to convert the given half-life from years to days. In a year, there are approximately 365.25 days (including leap years). So, we multiply the half-life (5.25 years) by the number of days in a year. \(5.25 \text{ years} = 5.25 \times 365.25 \approx 1917.5625 \text{ days}\)
03

Calculate Time for one-fourth Decay

Recall from Step 1, we stated that for one-fourth of the sample to remain, two half-lives should've passed. Therefore, we multiply the half-life in days with 2. \(2 \times 1917.5625 \approx 3835.125 \text{ days}\)

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Most popular questions from this chapter

Complete the following nuclear reactions. \begin{equation}a. _{5}^{12} \mathrm{B} \rightarrow_{6}^{12} \mathrm{C}+?\end{equation} \begin{equation}b. _{89}^{225} \mathrm{Ac} \longrightarrow_{87}^{221} \mathrm{Fr}+?\end{equation} \begin{equation}\mathbf{c.}_{28}^{63} \mathrm{Ni} \longrightarrow ?+_{-1}^{0} e\end{equation} \begin{equation}\mathbf{d} \cdot_{83}^{212} \mathrm{Bi} \rightarrow ?+_{2}^{4} \mathrm{He}\end{equation}

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