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Chapter 18: Problem 59

Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. \(_{19}^{45} \mathrm{K}\) b. \(\frac{56}{26} \mathrm{Fe}\) c. \(\frac{20}{11} \mathrm{Na}\) d. \(^{194}_{81} \mathrm{TI}\)

Short Answer

Expert verified
a. \(_{19}^{45} \mathrm{K}\) is likely unstable and would exhibit beta-minus decay. b. \(^{56}_{26} \mathrm{Fe}\) seems to be stable and would not exhibit radioactivity. c. \(^{20}_{11} \mathrm{Na}\) is likely unstable and would exhibit beta-plus decay. d. \(^{194}_{81} \mathrm{Tl}\) could be either stable or unstable, but if unstable, it would undergo alpha decay.

Step by step solution

01

a. \(_{19}^{45} \mathrm{K}\)

For potassium-45, the atomic number is 19 (protons), and the mass number is 45 (protons + neutrons). It has 26 neutrons. For nuclides with atomic numbers below 20, the ratio of neutrons to protons should be close to 1:1 for stability. In this case, the ratio is 26/19, which is higher than 1, so it is likely unstable. Since the neutron to proton ratio is too high, we would expect potassium-45 to exhibit beta-minus decay.
02

b. \(^{56}_{26} \mathrm{Fe}\)

For iron-56, the atomic number is 26 (protons), and the mass number is 56 (protons + neutrons). It has 30 neutrons. For a stable nuclide, the ratio of neutrons to protons should be around 1:1 at low atomic numbers and increase gradually for higher atomic numbers. The ratio for this nucleus is 30/26, which is about 1.15, so it seems stable. Since iron-56 appears to be stable, it would not exhibit radioactivity.
03

c. \(^{20}_{11} \mathrm{Na}\)

For sodium-20, the atomic number is 11 (protons), and the mass number is 20 (protons + neutrons). It has 9 neutrons. For nuclides with atomic numbers below 20, the ratio of neutrons to protons should be close to 1:1 for stability. The ratio for this nucleus is 9/11, which is less than 1, so it is likely unstable. Since the neutron to proton ratio is too low, we would expect sodium-20 to exhibit beta-plus decay.
04

d. \(^{194}_{81} \mathrm{Tl}\)

For thallium-194, the atomic number is 81 (protons), and the mass number is 194 (protons + neutrons). It has 113 neutrons. For a stable nuclide, the ratio of neutrons to protons should be around 1:1 at low atomic numbers and increase gradually for higher atomic numbers. The ratio for this nucleus is 113/81, which is about 1.4, so it could be either stable or unstable. However, since the atomic number is above 82, we would expect thallium-194 to undergo alpha decay if it is unstable.

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Most popular questions from this chapter

Iodine-131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.0 days. If a patient with thyroid disease consumes a sample of \(\mathrm{Na}^{131}\) I containing \(10 . \mu \mathrm{g}^{131} \mathrm{I}\) how long will it take for the amount of \(^{131}\) I to decrease to \(1 / 100\) of the original amount?

The mass ratios of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K}\) also can be used to date geologic materials. Potassium-40 decays by two processes: $$\begin{aligned} &_{19}^{40} \mathrm{K}+_{-1}^{0} \mathrm{e} \longrightarrow_{18}^{40} \mathrm{Ar}(10.7 \%) \quad t_{1 / 2}=1.27 \times 10^{9} \text { years }\\\ &_{19}^{40} \mathrm{K} \longrightarrow_{20}^{40} \mathrm{Ca}+_{-1}^{0} \mathrm{e}(89.3 \%) \end{aligned}$$a. Why are \(^{40} \mathrm{Ar} /^{40} \mathrm{K}\) ratios used to date materials rather than \(^{40} \mathrm{Ca} /^{40} \mathrm{K}\) ratios? b. What assumptions must be made using this technique? c. A sedimentary rock has an \(^{40} \mathrm{Ar} /^{40} \mathrm{K}\) ratio of 0.95. Calculate the age of the rock. d. How will the measured age of a rock compare to the actual age if some \(^{40}\) Ar escaped from the sample?

The bromine- 82 nucleus has a half-life of \(1.0 \times 10^{3}\) min. If you wanted \(1.0 \mathrm{g}^{82} \mathrm{Br}\) and the delivery time was 3.0 days, what mass of NaBr should you order (assuming all of the Br in the NaBr was \(\left.^{82} B r\right) ?\)

When using a Geiger-Müller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the Geiger-Müller tube to compare different measurements. Why?

At a flea market, you've found a very interesting painting done in the style of Rembrandt's "dark period" (1642-1672). You suspect that you really do not have a genuine Rembrandt, but you take it to the local university for testing. Living wood shows a carbon- 14 activity of 15.3 counts per minute per gram. Your painting showed a carbon- 14 activity of 15.1 counts per minute per gram. Could it be a genuine Rembrandt?
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