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Chapter 42: Q 9 Conceptual Question (page 1235)

The three isotopes
${}^{212}{Po}, {}^{137}{Cs}, and {}^{90}{Sr} decay as {}^{212}{Po} \to {}^{208}{Pb} + α, {}^{137}{Cs} \to {}^{137}{Ba} + e^{-} + γ, and {}^{90}{Sr} \to {}^{90}Y + e^{-}$ Which of these isotopes would be most useful as a biological tracer? Why?

Short Answer

Expert verified

Thus, $C s^{137}$ would be quite valuable.

Step by step solution

01

Given information

Three isotopes are given:

${}^{212}{Po}, {}^{137}{Cs}, and {}^{90}{Sr} decay as {}^{212}{Po} \to {}^{208}{Pb} + α, {}^{137}{Cs} \to {}^{137}{Ba} + e^{-} + γ, and {}^{90}{Sr} \to {}^{90}Y + e^{-}$

02

Explanation

Because a gamma ray is emitted after beta decay, $C s^{137}$ would be quite valuable. Because alphas and betas do not penetrate material well, they would not be discovered if they were to escape the body.

03

Explanation

However, the gamma ray does enter material well and might be identified if it were to escape the body.

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Most popular questions from this chapter

What is the total energy (in MeV) released in the beta-minus

decay of ³H?

Alpha decay occurs when an alpha particle tunnels through the Coulomb barrier. FIGURE CP42.63 shows a simple one-dimensional model of the potential-energy well of an alpha particle in a nucleus with A ≈ 235. The 15 fm width of this one-dimensional potential-energy well is the diameter of the nucleus. Further, to keep the model simple, the Coulomb barrier has been modeled as a 20-fm-wide, 30-MeV-high rectangular potential-energy barrier. The goal of this problem is to calculate the half-life of an alpha particle in the energy level E = 5.0 MeV. a. What is the kinetic energy of the alpha particle while inside the nucleus? What is its kinetic energy after it escapes from the nucleus? b. Consider the alpha particle within the nucleus to be a point particle bouncing back and forth with the kinetic energy you found in part a. What is the particle’s collision rate, the number of times per second it collides with a wall of the potential? c. What is the tunneling probability Ptunnel ?

The uranium isotope ${}^{238}U$ is naturally present at low levels in many soils. One of the nuclei in the decay series of ${}^{238}U$ is the radon isotope ${}^{222}R n$ , which decays by emitting a localid="1650487447445" $5.50 M e V$ alpha particle with localid="1650487458663" $t_{1 / 2} = 3.82$ days. Radon is a gas, and it tends to seep from soil into basements. The Environmental Protection Agency recommends that homeowners take steps to remove radon, by pumping in fresh air, if the radon activity exceeds $4 p C i p e r l i t e r$ of air.

a. How many ${}^{222}R n$ atoms are there in $1 m^{3}$ of air if the activity is $4 \frac{p C i}{L}$ ?

b. The range of alpha particles in air is $\approx 3 c m$ . Suppose we model a person as a $180 - c m$ -tall, $25 - c m$ -diameter cylinder with a mass of $65 k g$ . Only decays within $3 c m$ of the cylinder can cause exposure, and only $\approx 50 %$ , of the decays direct the alpha particle toward the person. Determine the dose in $m S v p e r y e a r$ for a person who spends the entire year in a room where the activity is $4 p C i / L$ .

c. Does the EPA recommendation seem appropriate? Why?

What is the age in years of a bone in which the $^{14} C^{12} C$ ratio is measured to be $1.65 \times 10^{- 13}$ ?

How many half-lives must elapse until (a) $90 %$ and (b) $99 %$ of a radioactive sample of atoms has decayed?

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