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Chapter 21: Problem 29

Strontium- 90 is one of the products of the fission of uranium- \(235 .\) This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for \(1.00 \mathrm{~g}\) of the isotope to be reduced to \(0.200 \mathrm{~g}\) by decay.

Short Answer

Expert verified
It will take 65.2 years for 1 gram of Strontium-90 to be reduced to 0.2 grams through decay.

Step by step solution

01

Determine the Number of Half-Lives

First, we need to determine how many half-lives it takes for 1g of the isotope to be reduced to 0.2g. This is done by dividing the final mass by the initial mass. Given that the initial mass is 1g and the final mass is 0.2g, we use the equation \(N = \log(0.2) / \log(0.5)\) to find that \(N = 2.322\), where \(N\) is the number of half-lives.
02

Determine the Total Time

Now we need to convert the number of half-lives to the total time it would take for the decay. This is done by multiplying the number of half-lives by the half-life of the isotope. Given that the half-life of Strontium-90 is 28.1 years, we use the equation \(T = N \cdot T_{\frac{1}{2}}\) to find that \(T = 2.322 \times 28.1 = 65.2\) years, where \(T\) is the total time.

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Most popular questions from this chapter

The quantity of a radioactive material is often measured by its activity (measured in curies or millicuries) rather than by its mass. In a brain scan procedure, a 70 -kg patient is injected with \(20.0 \mathrm{mCi}\) of \({ }^{99 \mathrm{~m}} \mathrm{Tc}\) which decays by emitting \(\gamma\) -ray photons with a halflife of \(6.0 \mathrm{~h}\). Given that the \(\mathrm{RBE}\) of these photons is 0.98 and only two-thirds of the photons are absorbed by the body, calculate the rem dose received by the patient. Assume all of the \({ }^{99 \mathrm{~m}}\) Tc nuclei decay while in the body. The energy of a gamma photon is \(2.29 \times 10^{-14} \mathrm{~J}\).

Explain how an atomic bomb works.

Explain the functions of a moderator and a control rod in a nuclear reactor.

Why do heavy elements such as uranium undergo fission while light elements such as hydrogen and lithium undergo fusion?

A radioactive substance undergoes decay as: $$ \begin{array}{cc} \text { Time (days) } & \text { Mass (g) } \\ \hline 0 & 500 \\ 1 & 389 \\ 2 & 303 \\ 3 & 236 \\ 4 & 184 \\ 5 & 143 \\ 6 & 112 \end{array} $$ Calculate the first-order decay constant and the halflife of the reaction.
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