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43.13. What nuclide is produced in the following radioactive decays? (a) \(\alpha\) decay of \(^{239}_{4} \mathrm{Pu}\) (b) \(\beta^{-}\) decay of \(^{24} \mathrm{Na}\) (c) \(\beta^{+}\) decay of \(\frac{15}{8} 0\)

Short Answer

Expert verified
(a) \( ^{235}_{92} \mathrm{U} \), (b) \( ^{24}_{12} \mathrm{Mg} \), (c) \( ^{15}_{7} \mathrm{N} \)

Step by step solution

01

Understand Alpha Decay

In alpha decay, an alpha particle, which consists of 2 protons and 2 neutrons, is emitted from the nucleus. This reduces the atomic number by 2 and the mass number by 4.
02

Apply Alpha Decay to Pu-239

For the decay of \( ^{239}_{4} \mathrm{Pu} \), the atomic number decreases from 94 to 92, and the mass number decreases from 239 to 235. The resulting nuclide is \( ^{235}_{92} \mathrm{U} \).
03

Understand Beta-Minus Decay

In beta-minus decay, a neutron is converted into a proton, resulting in an increase in the atomic number by 1. The mass number remains unchanged.
04

Apply Beta-Minus Decay to Na-24

For \( ^{24} \mathrm{Na} \), the atomic number increases from 11 to 12, while the mass number remains 24. The resulting nuclide is \( ^{24}_{12} \mathrm{Mg} \).
05

Understand Beta-Plus Decay

In beta-plus decay, a proton is converted into a neutron, decreasing the atomic number by 1, while the mass number remains unchanged.
06

Apply Beta-Plus Decay to O-15

For \( ^{15}_{8} \mathrm{O} \), the atomic number decreases from 8 to 7, with the mass number remaining at 15. The resulting nuclide is \( ^{15}_{7} \mathrm{N} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Alpha Decay
Alpha decay is a type of radioactive decay where an unstable atom releases an alpha particle. An alpha particle is composed of 2 protons and 2 neutrons, identical to a helium nucleus. When alpha decay occurs, the parent atom loses 4 units from its mass number and 2 units from its atomic number. This results in the formation of a new element.

For example, consider the alpha decay of plutonium-239, or \( ^{239}_{94} \text{Pu} \). During this process, the plutonium nucleus emits an alpha particle, leading to a reduction of its atomic number from 94 to 92 and its mass number from 239 to 235. Thus, the resulting daughter nucleus is uranium-235, or \( ^{235}_{92} \text{U} \).

Key points to remember:
  • Alpha particles are heavy and positively charged.
  • Alpha decay reduces atomic number by 2 and mass number by 4.
  • It is commonly seen in heavy elements like uranium and radium.
Beta-Minus Decay
In beta-minus (\(\beta^-\)) decay, a neutron is transformed into a proton within the nucleus, accompanied by the emission of an electron and an antineutrino. The transformation increases the atomic number by 1, but interestingly, the mass number remains the same. This is because the neutron and proton are similar in mass.

Applying this to sodium-24, or \( ^{24}_{11} \text{Na} \), a neutron within the sodium nucleus converts to a proton, which increases the atomic number by 1 from 11 to 12. Therefore, sodium transforms into magnesium-24, \( ^{24}_{12} \text{Mg} \).

What to note about beta-minus decay:
  • It increases the atomic number by 1.
  • The mass number remains unchanged.
  • It is a common decay mode in neutron-rich nuclei.
Beta-Plus Decay
Beta-plus (\(\beta^+\)) decay involves the conversion of a proton into a neutron, a positron (the antimatter equivalent of an electron), and a neutrino. Similar to beta-minus decay, the mass number remains unchanged. However, since a proton is converted to a neutron, the atomic number decreases by 1.

An example is the decay of oxygen-15, expressed as \(^{15}_{8}\text{O} \). In this decay, the atomic number is reduced from 8 to 7 as a proton in the oxygen nucleus transforms into a neutron, creating nitrogen-15, \(^{15}_{7}\text{N} \). The mass number, however, holds steady at 15.

Highlights of beta-plus decay include:
  • The atomic number decreases by 1.
  • The positron is emitted along with a neutrino.
  • This decay type is typical in proton-rich nuclides.

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Most popular questions from this chapter

43.22. Radioactive isotopes used in cancer therapy have a "shelf- life," like pharmaccuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of "Co is 5000 Ci. When its activity falls below 3500 \(\mathrm{Ci}\) , it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these "Co sources in your inventory was manufactured on October \(6,2004\) . It is now April \(6,2007\) . Is the source still usable? The half-life of \(^{6}\) Co is 5.271 years.

43.70. The nucleus \(\frac{15}{8} \mathrm{O}\) has a half-life of \(122.2 \mathrm{s} ; \mathrm{g} \mathrm{O}\) has a half-life of 26.9 s. If at some time a sample contains eqnal amounts of \(\frac{15}{8} \mathrm{O}\) and \(_{8}^{19} \mathrm{O}\) what is the ratio of \(_{8}^{15} 0\) to \(_{8}^{19} \mathrm{O}\) (b) after 15.0 minutes?

43.39. A \(50-\mathrm{kg}\) person accidentally ingests 0.35 \(\mathrm{Ci}\) of tritium. (a) Assume that the tritium spreads uniformly throughout the body. and that each decay leads on the average to the absorption of 5.0 keV of energy from the electrons emitted in the decay. The half-life of tritium is 12.3 \(\mathrm{y}\) , and the RBE of the electrons is \(1.0 .\) Calculate the absorbed dose in rad and the equivalent dose in rem during one week. (b) The \(\beta^{-}\) decay of tritium releases more than 5.0 keV of energy. Why is the average energy absorbed less than the total energy released in the decay?

43.1. How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, \(_{14}^{28} \operatorname{si} :(b)\) rubidium, \(\frac{85}{37} R b ;(c)\) thallinum, 205 \(\mathrm{TH} ?\)

43.8. Calculate (a) the total binding energy and (b) the binding energy per nucleon of \(^{12} \mathrm{C}\) (c) What percent of the rest mass of this nucleus is its total binding energy?

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