The nucleus of 150 decays by electron capture. Disregarding the daughter's recoil, determine the energy of the neutrino.
The nucleus of 150 decays by electron capture. Disregarding the daughter's recoil, determine the energy of the neutrino.
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![**Electron Capture and Energy of Neutrino Calculation**
*Problem Statement:*
The nucleus of \( \text{Iodine-50 (}^{50}\text{I}) \) decays by electron capture. Disregarding the recoil of the daughter nucleus, determine the energy of the neutrino.
*Solution Approach:*
1. **Understanding Electron Capture (EC):**
- In electron capture, an inner atomic electron is captured by the nucleus.
- A proton is converted into a neutron, and a neutrino is emitted.
- The general decay equation is:
\[
_Z^A \text{X} + e^- \rightarrow _{Z-1}^A \text{Y} + \nu_e
\]
where \( _Z^A \text{X} \) is the parent nucleus, \( _{Z-1}^A \text{Y} \) is the daughter nucleus, \( e^- \) is the captured electron, and \( \nu_e \) is the emitted neutrino.
2. **Energy Considerations:**
- The energy released (Q value) during this process is given by:
\[
Q = (m(\text{parent}) + m_e - m(\text{daughter}))c^2
\]
where \( m(\text{parent}) \) is the mass of the parent atom, \( m_e \) is the mass of the electron, and \( m(\text{daughter}) \) is the mass of the daughter atom. \( c \) is the speed of light in vacuum.
- For simplicity, if we disregard the daughter nucleus's recoil, almost all the Q value is taken by the neutrino.
3. **Calculations:**
- Assuming the masses are provided or calculated according to atomic mass units (AMU), convert them to the energy equivalent using \( 1 \text{ AMU} \approx 931.5 \text{ MeV}/c^2 \).
4. **Conclusion:**
- The calculated Q value will be approximately the energy of the neutrino.
**Graphical Representation:**
*Since there are no graphs or diagrams in this image, there is no need for further illustration.*
This problem involves a detailed understanding of nuclear physics, particularly the process of electron capture and energy transformation. The solution provides a step-by-step approach to determine the energy of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fdfc26a-e6d8-4dfd-b2bf-654dccb4509d%2F9d0fad1e-44b1-41ed-9440-bae47b45164b%2Ft1ku9e_processed.png&w=3840&q=75)
Transcribed Image Text:**Electron Capture and Energy of Neutrino Calculation**
*Problem Statement:*
The nucleus of \( \text{Iodine-50 (}^{50}\text{I}) \) decays by electron capture. Disregarding the recoil of the daughter nucleus, determine the energy of the neutrino.
*Solution Approach:*
1. **Understanding Electron Capture (EC):**
- In electron capture, an inner atomic electron is captured by the nucleus.
- A proton is converted into a neutron, and a neutrino is emitted.
- The general decay equation is:
\[
_Z^A \text{X} + e^- \rightarrow _{Z-1}^A \text{Y} + \nu_e
\]
where \( _Z^A \text{X} \) is the parent nucleus, \( _{Z-1}^A \text{Y} \) is the daughter nucleus, \( e^- \) is the captured electron, and \( \nu_e \) is the emitted neutrino.
2. **Energy Considerations:**
- The energy released (Q value) during this process is given by:
\[
Q = (m(\text{parent}) + m_e - m(\text{daughter}))c^2
\]
where \( m(\text{parent}) \) is the mass of the parent atom, \( m_e \) is the mass of the electron, and \( m(\text{daughter}) \) is the mass of the daughter atom. \( c \) is the speed of light in vacuum.
- For simplicity, if we disregard the daughter nucleus's recoil, almost all the Q value is taken by the neutrino.
3. **Calculations:**
- Assuming the masses are provided or calculated according to atomic mass units (AMU), convert them to the energy equivalent using \( 1 \text{ AMU} \approx 931.5 \text{ MeV}/c^2 \).
4. **Conclusion:**
- The calculated Q value will be approximately the energy of the neutrino.
**Graphical Representation:**
*Since there are no graphs or diagrams in this image, there is no need for further illustration.*
This problem involves a detailed understanding of nuclear physics, particularly the process of electron capture and energy transformation. The solution provides a step-by-step approach to determine the energy of
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