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Chapter 21: Problem 15

Decay of which nucleus will lead to the following products: \((\mathbf{a})\) bismuth-211 by beta decay; \((\mathbf{b})\) chromium-so by positron emission; \((\mathbf{c})\) tantalum-179 by electron capture; \((\mathbf{d})\) radium-226 by alpha decay?

Short Answer

Expert verified
The parent nuclei for each decay and their corresponding products are: a) Lead-211 (Pb-211) decays to Bismuth-211 (Bi-211) via beta decay. b) Manganese-50 (Mn-50) decays to Chromium-50 (Cr-50) via positron emission. c) Tungsten-179 (W-179) decays to Tantalum-179 (Ta-179) via electron capture. d) Thorium-230 (Th-230) decays to Radium-226 (Ra-226) via alpha decay.

Step by step solution

01

1. Beta decay

In beta decay, a neutron in the nucleus is converted into a proton, leading to the emission of an electron (beta particle). The mass number remains the same while the atomic number increases by 1. Given that the resulting nucleus is bismuth-211, let's find the parent nucleus. Let the parent nucleus be X. Since the atomic number of bismuth is 83, after beta decay, the atomic number of X must be 82. The mass number remains unchanged, so the mass number of X is also 211. Hence, the parent nucleus is lead-211 (Pb-211).
02

2. Positron emission

In positron emission, a proton is converted into a neutron, leading to the emission of a positron. The mass number remains the same while the atomic number decreases by 1. Given that the resulting nucleus is chromium-50, let's find the parent nucleus. Let the parent nucleus be Y. Since the atomic number of chromium is 24, before positron emission, the atomic number of Y must be 25. The mass number remains unchanged, so the mass number of Y is also 50. Hence, the parent nucleus is manganese-50 (Mn-50).
03

3. Electron capture

In electron capture, a proton in the nucleus captures a nearby electron and converts into a neutron. The mass number remains the same while the atomic number decreases by 1. Given that the resulting nucleus is tantalum-179, let's find the parent nucleus. Let the parent nucleus be Z. Since the atomic number of tantalum is 73, before electron capture, the atomic number of Z must be 74. The mass number remains unchanged, so the mass number of Z is also 179. Hence, the parent nucleus is tungsten-179 (W-179).
04

4. Alpha decay

In alpha decay, a nucleus emits an alpha particle, which consists of two protons and two neutrons. The mass number decreases by 4, while the atomic number decreases by 2. Given that the resulting nucleus is radium-226, let's find the parent nucleus. Let the parent nucleus be W. Since the atomic number of radium is 88, before alpha decay, the atomic number of W must be 90. The mass number decreases by 4, so the mass number of W is 230. Hence, the parent nucleus is thorium-230 (Th-230). In summary, the parent nuclei for each decay and their products are: a) Pb-211 ➝ Bi-211 (beta decay) b) Mn-50 ➝ Cr-50 (positron emission) c) W-179 ➝ Ta-179 (electron capture) d) Th-230 ➝ Ra-226 (alpha decay)

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Most popular questions from this chapter

A 65-kg person is accidentally exposed for 240 s to a 15-mCi source of beta radiation coming from a sample of \(^{90}\) Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of \(8.75 \times 10^{-14} \mathrm{J} .\) and 7.5\(\%\) of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. (c) If the RBE of the beta particles is \(1.0,\) what is the effective dose in mrem and in sieverts? (d) Is the radiation dose equal to, greater than, or less than that for a typical mammogram \((300\) mrem \() ?\)

Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. (a) How many beta particles are emitted in 600 s by a 3.75 -mg sample of \(^{60} \mathrm{Co} ?(\mathbf{b})\) What is the activity of the sample in \(\mathrm{Bq}\) ?

Hydroxyl radicals can pluck hydrogen atoms from molecules ("hydrogen abstraction"), and hydroxide ions can pluck protons from molecules (“deprotonation”). Write the reaction equations and Lewis dot structures for the hydrogen abstraction and deprotonation reactions for the generic carboxylic acid R-COOH with hydroxyl radical and hydroxide ion, respectively. Why is hydroxyl radical more toxic to living systems than hydroxide ion?

Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little \(^{235} U\) to be used as a fuel. (ii) \(^{238} U\) cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than 50\(\%^{235} \mathrm{U}\) in composition. (iv) The neutron-induced fission of \(^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \(^{238} \mathrm{U}\).

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of Nal, in which only a small fraction of the iodide is radioactive. (a) Why is Nal a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about 12\(\%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01\(\%\) of the original amount?
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