Problem 124
Question
Which of the following statements is/are incorrect, when the nuclide, \({ }_{19} \mathrm{~K}^{40}\), is subject to \(\mathrm{K}\)-electron capture? (a) \({ }^{40} \mathrm{Ar}\) is produced with emission of \(\beta\)-particle. (b) \({ }^{40} \mathrm{Ar}\) is produced with emission of \(\alpha\)-particles. (c) \({ }^{40} \mathrm{Ar}\) is produced without emission of radiation (d) \({ }^{40} \mathrm{Ar}\) is produced with emission of X-radiation.
Step-by-Step Solution
Verified Answer
Statements (a), (b), and (c) are incorrect.
1Step 1: Understanding K-Electron Capture
K-electron capture, or K-capture, is a type of radioactive decay in which an electron from the innermost energy level (the K shell) is captured by the nucleus. In this process, a proton is converted into a neutron with the emission of a neutrino. As a result, the atomic number decreases by one, while the mass number remains unchanged. Thus, \[{}^{40}_{19}\text{K} \rightarrow {}^{40}_{18}\text{Ar} \] but no \(\beta\)-particle is emitted in this process.
2Step 2: Analyzing Statement (a)
The statement (a) suggests \(^{40}\mathrm{Ar}\) is produced with \(\beta\)-particle emission. During K-electron capture, only a neutrino is emitted, not a \(\beta\)-particle. Hence, this statement is incorrect.
3Step 3: Analyzing Statement (b)
The statement (b) suggests \(^{40}\mathrm{Ar}\) is produced with \(\alpha\)-particle emission. K-electron capture does not involve \(\alpha\)-particle emission. Thus, this statement is incorrect.
4Step 4: Analyzing Statement (c)
The statement (c) mentions \(^{40}\mathrm{Ar}\) is produced without emission of radiation. However, neutrinos are emitted, and often X-rays or Auger electrons due to electron rearrangement following K-capture. Thus, this statement is incorrect because of potential radiation emission.
5Step 5: Analyzing Statement (d)
The statement (d) suggests \(^{40}\mathrm{Ar}\) is produced with emission of X-radiation. During K-capture, inner electron vacancies often lead to the emission of X-rays due to electronic transitions filling those vacancies. Therefore, this statement is correct.
Key Concepts
K-electron captureNeutrino emissionNuclear reactionsAtomic number change
K-electron capture
K-electron capture, also known as K-capture, is a fascinating nuclear process. This type of radioactive decay occurs when an electron from the innermost energy level, or the K shell, is captured by the nucleus of an atom. This leads to a proton in the nucleus being converted into a neutron. As a result, the atomic number of the element decreases by one because there is one less proton, while the mass number remains unchanged.
For example, in the case of the nuclide \({}_{19} \text{K}^{40}\), when it undergoes K-capture, it transforms into \({}_{18} \text{Ar}^{40}\). This transformation is guided by the need for the nucleus to reach a more stable state.
For example, in the case of the nuclide \({}_{19} \text{K}^{40}\), when it undergoes K-capture, it transforms into \({}_{18} \text{Ar}^{40}\). This transformation is guided by the need for the nucleus to reach a more stable state.
- No \(\beta\)-particle emission occurs during K-capture.
- It does emit a neutrino.
Neutrino emission
During the K-electron capture process, the emission of a neutrino is a key event. Neutrinos are incredibly tiny, neutral particles that have very little mass and interact weakly with matter, making them extremely difficult to detect. However, their role is vital in conserving energy and momentum during nuclear transformations.
When the captured electron merges with a proton to form a neutron, the neutrino carries away the energy difference between the initial and final states. This helps to maintain the balance in the energy equation of the reaction. In our example of potassium, \({}_{19} \text{K}^{40}\) capturing a K-electron leads to the production of \({}_{18} \text{Ar}^{40}\) while emitting a neutrino. This subtle emission often goes unnoticed in other reactions but is integral to nuclear changes.
When the captured electron merges with a proton to form a neutron, the neutrino carries away the energy difference between the initial and final states. This helps to maintain the balance in the energy equation of the reaction. In our example of potassium, \({}_{19} \text{K}^{40}\) capturing a K-electron leads to the production of \({}_{18} \text{Ar}^{40}\) while emitting a neutrino. This subtle emission often goes unnoticed in other reactions but is integral to nuclear changes.
Nuclear reactions
Nuclear reactions represent the events when nucleus compositions are altered, either naturally or artificially. These reactions are fundamental in changing one element into another through various paths such as radioactive decay, fission, and fusion.
K-electron capture is a specific type of nuclear reaction. In this process, the interaction between a captured electron and a proton results in the formation of a neutron and a neutrino emission. The captured electron initiates this transformation by reducing the atomic number of the nuclide, changing the element without altering the mass number.
K-electron capture is a specific type of nuclear reaction. In this process, the interaction between a captured electron and a proton results in the formation of a neutron and a neutrino emission. The captured electron initiates this transformation by reducing the atomic number of the nuclide, changing the element without altering the mass number.
- Nuclear reactions like this often involve energy changes.
- They can lead to the emission of neutrinos or radiation like X-rays.
Atomic number change
One critical outcome of a nuclear reaction like the K-electron capture is the change in the atomic number of the element involved.
The atomic number is crucial because it defines the identity of the element, representing the number of protons in the nucleus.
A change in this number means the element itself can transform into another.
In K-electron capture, the atomic number decreases by one when a proton is converted into a neutron. For instance, when potassium-40 undergoes K-capture, its atomic number changes from 19 to 18 transforming into argon-40. While the atomic number changes, the mass number remains the same because the total number of nucleons (protons and neutrons) in the nucleus stays constant.
In K-electron capture, the atomic number decreases by one when a proton is converted into a neutron. For instance, when potassium-40 undergoes K-capture, its atomic number changes from 19 to 18 transforming into argon-40. While the atomic number changes, the mass number remains the same because the total number of nucleons (protons and neutrons) in the nucleus stays constant.
- The identity of the element is determined by its atomic number.
- Changes in atomic number can lead to different chemical properties and interactions.
Other exercises in this chapter
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