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Magazine Chapter 25: Problem 49
Complete the following reactions: (a) \({ }^{158} \mathrm{Tm}+\beta^{-} \rightarrow\) ____ (b) \({ }^{178} \mathrm{Hf} \rightarrow{ }^{178} \mathrm{Lu}+\) _____ (c) \({ }^{216} \mathrm{Fr} \rightarrow{ }^{212} \mathrm{At}+\) _____ (d) \({ }^{8} \mathrm{Be} \rightarrow\) _____ \(+{ }^{4} \mathrm{He}\)
Short Answer
Expert verified
(a) Yb (b) \(\beta^+\) (c) \(^4He\) (d) \(^4He\)
Step by step solution
01
Understand Beta Minus Decay
In beta minus decay, a neutron is transformed into a proton with the emission of an electron (beta particle, \(\beta^-\)) and an antineutrino. This results in the increase of the atomic number by 1 while mass number remains constant.
02
Solve Reaction (a)
For \( {}^{158} \mathrm{Tm} + \beta^- \rightarrow\), apply beta minus decay where the atomic number increases by 1. Tm (thulium) has an atomic number of 69, so it becomes element 70, which is ytterbium (Yb). Thus, the reaction is \( {}^{158} \mathrm{Tm} + \beta^- \rightarrow {}^{158} \mathrm{Yb} \).
03
Understand Electron Capture
Electron capture involves a proton in the nucleus capturing an inner-shell electron and converting into a neutron. This results in the decrease of the atomic number by 1, while the mass number stays the same.
04
Solve Reaction (b)
Longer decay chain reactions, such as electron capture and beta decay, apply where \( {}^{178} \mathrm{Hf} \rightarrow {}^{178} \mathrm{Lu} + \text{some particle}\). Since the atomic number decreases by 1, this means beta plus decay is involved and a positron \(\beta^+\) or electron capture occurs. Thus the completed reaction is \( {}^{178} \mathrm{Hf} \rightarrow {}^{178} \mathrm{Lu} + \beta^+ \).
05
Understand Alpha Decay
Alpha decay involves the loss of 2 protons and 2 neutrons (an alpha particle, \( {}^{4} \mathrm{He} \)) from the nucleus. This decreases the mass number by 4 and the atomic number by 2.
06
Solve Reaction (c)
\( {}^{216} \mathrm{Fr} \rightarrow {}^{212} \mathrm{At} + \text{some particle}\). The mass number decreases by 4, indicating an alpha particle \( {}^4 \mathrm{He}\). Hence, the reaction is \( {}^{216} \mathrm{Fr} \rightarrow {}^{212} \mathrm{At} + {}^{4} \mathrm{He} \).
07
Solve Reaction (d)
\( {}^{8} \mathrm{Be} \rightarrow \text{some particle} + {}^{4} \mathrm{He}\). Since the mass number of Be is 8 and a helium nucleus has a mass number of 4, the other product must also be \( {}^{4} \mathrm{He} \). Therefore, \( {}^{8} \mathrm{Be} \rightarrow {}^{4} \mathrm{He} + {}^{4} \mathrm{He}\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Beta Decay
Beta decay is a type of nuclear reaction that's crucial for understanding how certain elements transform into others within radioactive processes. It occurs when a nucleus is unstable and needs to reach a more stable state. There are two types: beta minus decay and beta plus decay.
**Beta Minus Decay:**- In beta minus decay, a neutron in an atom's nucleus is converted into a proton.- As a result, the atom releases a fast-moving electron, called a beta particle (denoted as \( \beta^- \)), and an antineutrino.- Importantly, the atomic number of the element increases by 1 because a neutron becomes a proton while the mass number remains constant.
Example: - A thulium atom, with atomic number 69, upon undergoing beta minus decay turns into ytterbium, with atomic number 70.
**Key Factors:**- Beta decay allows elements to transform into a different element.- It is one way that radiation can interact with and change matter.
**Beta Minus Decay:**- In beta minus decay, a neutron in an atom's nucleus is converted into a proton.- As a result, the atom releases a fast-moving electron, called a beta particle (denoted as \( \beta^- \)), and an antineutrino.- Importantly, the atomic number of the element increases by 1 because a neutron becomes a proton while the mass number remains constant.
Example: - A thulium atom, with atomic number 69, upon undergoing beta minus decay turns into ytterbium, with atomic number 70.
**Key Factors:**- Beta decay allows elements to transform into a different element.- It is one way that radiation can interact with and change matter.
Alpha Decay
Alpha decay is another type of radioactive decay where the nucleus emits an alpha particle to become more stable. This process leads to a significant shift in the identity of the original atom.
**Understanding Alpha Particles:**- An alpha particle consists of 2 protons and 2 neutrons bound together. - This is essentially the same as a helium nucleus, noted as \( {}^4 \mathrm{He} \).
**Process of Alpha Decay:**- During alpha decay, the emitting nucleus loses these four nucleons.- Consequently, its atomic number decreases by 2 and its mass number decreases by 4.
**Example: **- Francium-216 undergoing alpha decay results in astatine-212 as it loses an alpha particle.
**Significance:**- Alpha decay is a key process in the decay chains of heavy elements.- It's essential for understanding the transformations in natural and synthetic radioactive processes.
**Understanding Alpha Particles:**- An alpha particle consists of 2 protons and 2 neutrons bound together. - This is essentially the same as a helium nucleus, noted as \( {}^4 \mathrm{He} \).
**Process of Alpha Decay:**- During alpha decay, the emitting nucleus loses these four nucleons.- Consequently, its atomic number decreases by 2 and its mass number decreases by 4.
**Example: **- Francium-216 undergoing alpha decay results in astatine-212 as it loses an alpha particle.
**Significance:**- Alpha decay is a key process in the decay chains of heavy elements.- It's essential for understanding the transformations in natural and synthetic radioactive processes.
Electron Capture
Electron capture is a fascinating process used by unstable atoms to stabilize themselves. It involves an interaction right within the nucleus and changes the identity of the element.
**What Happens During Electron Capture?** - The nucleus of an atom captures an electron from its own electron cloud, often an inner shell electron. - This captured electron combines with a proton to form a neutron, thereby decreasing the atomic number by 1. - The mass number, however, remains unchanged.
**Why Does It Happen?** - It occurs when positive charges outweigh and the nucleus needs to stabilize by reducing the overall electrical charge.
**Practical Example:** - An example is hafnium-178 turning into lutetium-178 through electron capture, resulting in the emission of a neutrino.
**Relevance of Electron Capture:** - It's a critical mechanism by which atoms adjust their composition to achieve stability. - Essential for many biological processes and applications in nuclear medicine.
**What Happens During Electron Capture?** - The nucleus of an atom captures an electron from its own electron cloud, often an inner shell electron. - This captured electron combines with a proton to form a neutron, thereby decreasing the atomic number by 1. - The mass number, however, remains unchanged.
**Why Does It Happen?** - It occurs when positive charges outweigh and the nucleus needs to stabilize by reducing the overall electrical charge.
**Practical Example:** - An example is hafnium-178 turning into lutetium-178 through electron capture, resulting in the emission of a neutrino.
**Relevance of Electron Capture:** - It's a critical mechanism by which atoms adjust their composition to achieve stability. - Essential for many biological processes and applications in nuclear medicine.
