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Write a nuclear \(\beta^{-}\) decay reaction that produces the \(^{90} \mathrm{Y}\) nucleus. (Hint: The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested.)

Short Answer

Expert verified
The nuclear 尾鈦 decay reaction that produces the \(^{90}\mathrm{Y}\) nucleus is given by: \[{}^{90}\mathrm{Sr} \rightarrow ^{90}\mathrm{Y} + e鈦 + \bar{\nu}_e\]

Step by step solution

01

Identify the parent nuclide

Based on the hint provided, we know that the parent nuclide has similar chemistry to calcium and is a major waste product of reactors. We can identify this nuclide as \(^{90}\mathrm{Sr}\), which is a well-known radioisotope produced in nuclear reactors.
02

Understand 尾鈦 decay

In 尾鈦 decay, a neutron in the nucleus is converted into a proton, an electron (also known as a beta particle), and an electron antineutrino. The emitted beta particle and the electron antineutrino carry away some energy from the nucleus. We can represent this conversion in the neutron-to-proton transformation process using the following reaction: \[n \rightarrow p + e鈦 + \bar{\nu}_e\]
03

Write the 尾鈦 decay equation for the parent nuclide

Now that we know the parent nuclide \(^{90}\mathrm{Sr}\) and the fundamental process of 尾鈦 decay, we can write the nuclear 尾鈦 decay equation. As \(^{90}\mathrm{Sr}\) undergoes 尾鈦 decay, one of its neutrons will convert into a proton, increasing the atomic number (which identifies the element) by 1 while the mass number remains the same. This will result in the formation of the \(^{90}\mathrm{Y}\) nucleus. The full decay equation is as follows: \[^{90}\mathrm{Sr} \rightarrow ^{90}\mathrm{Y} + e鈦 + \bar{\nu}_e\] In conclusion, we have written the nuclear 尾鈦 decay reaction that produces the \(^{90}\mathrm{Y}\) nucleus starting from the parent nuclide \(^{90}\mathrm{Sr}\). The final equation representing this reaction is given by: \[^{90}\mathrm{Sr} \rightarrow ^{90}\mathrm{Y} + e鈦 + \bar{\nu}_e\]

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Key Concepts

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

Nuclear Reactions
Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of elements. Unlike chemical reactions, where only electrons are involved, nuclear reactions impact the core of the atom, which holds protons and neutrons. These changes can lead to the creation of new elements or isotopes.
In the realm of nuclear reactions, there are two main types: fusion and fission. Another important subcategory includes radioactive decay, where unstable nuclei lose energy by emitting radiation. A common type of decay is \(\beta^-\) decay, where a neutron is converted into a proton, an electron (beta particle), and an electron antineutrino.
To write a nuclear reaction equation, one must balance the atomic and mass numbers on both sides. This ensures that the principle of conservation of both mass and charge is adhered to. For example, in the \(\beta^-\) decay of \(^{90}\mathrm{Sr}\) into \(^{90}\mathrm{Y}\), the mass number remains 90, but the atomic number increases by one as a neutron becomes a proton.
Radioisotopes
Radioisotopes are isotopes of elements that are unstable and exhibit radioactivity. This instability occurs because of an imbalance in the number of protons and neutrons in the atom's nucleus. As a result, radioisotopes tend to decay over time by emitting ionizing radiation in the form of alpha, beta, or gamma rays.
\(^{90}\mathrm{Sr}\) is a notable radioisotope. It is an isotope of strontium and often emerges as a by-product in nuclear reactors. Its chemical properties are similar to calcium, making it a concern for human health as it can accumulate in bones when ingested.
Radioisotopes have varying stability and half-lives, which is the time it takes for half of a sample to decay. This property makes them useful in various applications such as in medical diagnostics, treatment (like cancer radiotherapy), and even food preservation by irradiation.
  • They help in radiometric dating to determine the age of materials.
  • They serve as tracers in biological and chemical research.
Nuclear Chemistry
Nuclear chemistry is the study of the chemical and physical properties of elements as influenced by nuclear and radioactive processes. This branch of chemistry plays a crucial role in discovering the applications and effects of radioactivity and isotopic change.
It encompasses the study of phenomena such as radioactive decay, fission, and fusion. In particular, the study of nuclear reactions like \(\beta^-\) decay is important in understanding how elements transform under certain conditions.
Beta decay is an integral concept in nuclear chemistry. Here, it's crucial to note that the element undergoing decay changes its atomic number but typically retains its mass number. This reaction reveals insights into the balance of forces within a nucleus and the conservation of certain properties like angular momentum.
Nuclear chemists use this knowledge to innovate and tackle challenges such as nuclear waste management, where understanding decay processes can help in devising methods to reduce environmental and biological impacts.
  • They work on developing nuclear power sources that are safer and more efficient.
  • Nuclear chemistry aids in medical advancements, particularly in the development of diagnostic tools and treatments using radioisotopes.

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Most popular questions from this chapter

Explain the difference between nuclear fission and nuclear fusion.

A rare decay mode has been observed in which \(^{222} \mathrm{Ra}\) emits a \(^{14} \mathrm{C}\) nucleus. (a) The decay equation is \(^{222} \mathrm{Ra} \rightarrow^{A} \mathrm{X}+^{14} \mathrm{C} .\) Identify the nuclide \(^{A} \mathrm{X} .\) (b) Find the energy emitted in the decay. The mass of \(222 \mathrm{Ra}\) is 222.015353 u.

A radioactive sample initially contains \(2.40 \times 10^{-2}\) mol of a radioactive material whose half-life is 6.00 h. How many moles of the radioactive material remain after \(6.00 \mathrm{h}\) ? After 12.0 h? After 36.0 h?

Another set of reactions that fuses hydrogen into helium in the Sun and especially in hotter stars is called the CNO cycle: $$\begin{aligned} &^{12} \mathrm{C}+^{1} \mathrm{H} \rightarrow^{13} \mathrm{N}+\gamma\\\ &^{13} \mathrm{N} \rightarrow^{13} \mathrm{C}+e^{+}+v_{\mathrm{e}}\\\ &^{13} \mathrm{C}+^{1} \mathrm{H} \rightarrow^{14} \mathrm{N}+\gamma\\\ &^{14} \mathrm{N}+^{1} \mathrm{H} \rightarrow^{15} \mathrm{O}+\gamma\\\ &^{15} \mathrm{O} \rightarrow^{15} \mathrm{N}+e^{+}+v_{\mathrm{e}}\\\ &^{15} \mathrm{N}+^{1} \mathrm{H} \rightarrow^{12} \mathrm{C}+^{4} \mathrm{He} \end{aligned}$$ This process is a "cycle" because \(^{12} \mathrm{C}\) appears at the beginning and end of these reactions. Write down the overall effect of this cycle (as done for the proton-proton chain in \(2 e^{-}+4^{1} \mathrm{H} \rightarrow^{4} \mathrm{He}+2 v_{\mathrm{e}}+6 \gamma\) ). Assume that the positrons annihilate electrons to form more \(\gamma\) rays.

The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0\% efficiency in converting nuclear power to electrical power. (a) What is the thermal nuclear power output in megawatts? (b) How many \(^{235}\) U nuclei fission each second, assuming the average fission produces \(200 \mathrm{MeV}\) ? (c) What mass of \(^{235} \mathrm{U}\) is fissioned in 1 year of full-power operation?

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