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What happens to the atomic number when an electron fuses with a proton?
What happens to the atomic number when an electron fuses with a proton?
Why is the energy spectrum of beta particles not well-defined?
Why is the energy spectrum of beta particles not well-defined?
Which type of radiation results in the highest energy loss from a nucleus?
Which type of radiation results in the highest energy loss from a nucleus?
How is the decay constant ($, \lambda$) related to the average lifetime ($\tau$) of a radioactive nucleus?
How is the decay constant ($, \lambda$) related to the average lifetime ($\tau$) of a radioactive nucleus?
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What mathematical function describes the time course of radioactive decay?
What mathematical function describes the time course of radioactive decay?
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At which point in the decay curve is the number of undecayed nuclei equal to approximately 37% of the initial value?
At which point in the decay curve is the number of undecayed nuclei equal to approximately 37% of the initial value?
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What is represented by the variable $T_{1/2}$ in the decay formula?
What is represented by the variable $T_{1/2}$ in the decay formula?
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What type of particle is emitted alongside a beta particle in beta decay?
What type of particle is emitted alongside a beta particle in beta decay?
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What is the remaining fraction of undecayed nuclei after a time period equal to three times the half-life?
What is the remaining fraction of undecayed nuclei after a time period equal to three times the half-life?
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What method is suggested for accurately determining the average lifetime from a decay graph?
What method is suggested for accurately determining the average lifetime from a decay graph?
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What does the effective decay constant (
abla_eff) represent?
What does the effective decay constant ( abla_eff) represent?
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Why is determining the effective half-life significant in the context of radioactive pharmacons?
Why is determining the effective half-life significant in the context of radioactive pharmacons?
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What does the slope of the semi-logarithmic plot represent in the decay analysis?
What does the slope of the semi-logarithmic plot represent in the decay analysis?
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What are two primary ways the amount of radioactive nuclei can decrease in a patient's body?
What are two primary ways the amount of radioactive nuclei can decrease in a patient's body?
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How do you determine the slope from the plotted graph of
ln(N) vs elapsed time?
How do you determine the slope from the plotted graph of ln(N) vs elapsed time?
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What is the relationship between effective decay, biological decay, and physical decay?
What is the relationship between effective decay, biological decay, and physical decay?
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What effect does the asymmetrical distribution of nucleons have on binding energy?
What effect does the asymmetrical distribution of nucleons have on binding energy?
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In the shell model, what prohibits neutrons from occupying proton energy states?
In the shell model, what prohibits neutrons from occupying proton energy states?
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What is indicated by the presence of magic numbers in nuclei?
What is indicated by the presence of magic numbers in nuclei?
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For light nuclei, what ratio of neutrons to protons (N/Z) is considered optimal for stability?
For light nuclei, what ratio of neutrons to protons (N/Z) is considered optimal for stability?
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What primary limitation does the shell model for nuclei exhibit?
What primary limitation does the shell model for nuclei exhibit?
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What is the configuration of nucleons in the 1s shell according to the model?
What is the configuration of nucleons in the 1s shell according to the model?
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Which features are similar between atomic and nuclear shells?
Which features are similar between atomic and nuclear shells?
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What happens to binding energy as the number of neutrons in a nucleus becomes disproportionately higher than protons?
What happens to binding energy as the number of neutrons in a nucleus becomes disproportionately higher than protons?
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What type of decay occurs in the parent element of a radioactive decay series?
What type of decay occurs in the parent element of a radioactive decay series?
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What is the formula to determine the mass number of members in a radioactive series?
What is the formula to determine the mass number of members in a radioactive series?
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What do you get when you fix the neutron number and move parallel to the Z axis?
What do you get when you fix the neutron number and move parallel to the Z axis?
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Which of the following isotopes is radioactive and ejects beta negative particles?
Which of the following isotopes is radioactive and ejects beta negative particles?
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What is the nucleon mass number (A) composed of in a nucleus?
What is the nucleon mass number (A) composed of in a nucleus?
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Which isotope of carbon is commonly used in carbon dating due to its half-life?
Which isotope of carbon is commonly used in carbon dating due to its half-life?
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What does the mass number (A) represent in the context of the nucleus?
What does the mass number (A) represent in the context of the nucleus?
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How can the stability of nuclei be determined?
How can the stability of nuclei be determined?
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How does the addition of an extra neutron affect the stability of a nucleus?
How does the addition of an extra neutron affect the stability of a nucleus?
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Which region in the N-Z graph represents stable nuclei?
Which region in the N-Z graph represents stable nuclei?
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What process occurs in unstable nuclei with an N/Z ratio much higher than 1?
What process occurs in unstable nuclei with an N/Z ratio much higher than 1?
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What is indicated by the blue strip in the N-Z graph?
What is indicated by the blue strip in the N-Z graph?
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In terms of nuclear stability, what does the hatched elliptical area represent?
In terms of nuclear stability, what does the hatched elliptical area represent?
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Which term in the semiempirical model accounts for the decrease in binding energy due to surface nucleons?
Which term in the semiempirical model accounts for the decrease in binding energy due to surface nucleons?
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What is a significant aspect of the Weizsäcker formula for binding energy?
What is a significant aspect of the Weizsäcker formula for binding energy?
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Why are light nuclei unable to emit alpha particles?
Why are light nuclei unable to emit alpha particles?
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Study Notes
Nuclear Decay Processes
- Electron capture:
- Electron fuses with a proton in the nucleus, transforming it into a neutron.
- Atomic number decreases by one, mass number remains unchanged.
- Characteristic X-rays or Auger electrons are emitted.
- Energy quantization:
- Electrons in atoms absorb or emit energy in discrete portions (quanta).
- Energy levels of a bound electron are quantized.
- Energy of radioactive decays is characteristic for the parent nucleus, used for identification.
- Alpha decay has the highest energy loss, followed by beta and then gamma.
- Alpha and gamma decay energies are quantized and specific to the emitting nucleus.
- Beta decay energy is quantized, but its spectrum is continuous due to random energy distribution between beta particle and neutrino/antineutrino.
Radioactive Decay and Half-Life
- Radioactive decay:
- Number of parent nuclei decreases over time, following a negative exponential function.
- N(t) = N0 * e^(-λt) = N0 * e^(-t/τ), where:
- N(t) is the number of undecayed nuclei at time t.
- N0 is the initial number of nuclei.
- λ is the decay constant (rate constant).
- τ is the average lifetime of the nuclei.
- Half-life:
- Time taken for half of the radioactive nuclei to decay.
- N(t) = N0 * 2^(-t/T½), where T½ is the half-life.
- Graphical analysis:
- Semi-logarithmic plot (ln(N/N0) vs time) linearizes the exponential decay function, allowing for easier determination of the decay constant.
- Slope of the line equals -λ.
Effective Decay
- Radioactive pharmacons in living organisms undergo both physical and biological decay.
- Physical decay: Radioactive nucleus decays into a daughter nucleus, emitting β or γ rays.
- Biological decay: Radiopharmacon is removed from the body through excretion or exhalation.
- Effective decay: Combined effect of physical and biological decay.
- Effective decay constant (λeff): Sum of physical (λphys) and biological (λbiol) decay constants.
- Effective half-life: Lowest out of the three half-lives (physical, biological, and effective).
Radioactive Decay Chains/Series
- Naturally occurring radioactive elements are categorized into three decay chains.
- Parent element decays via alpha emission.
- Subsequent daughter elements can decay via alpha or beta emission.
- Mass number of each member follows the formula: A = 4n + C, where C = 0, 1, 2, or 3.
Nuclear Structure and Stability
- Nucleus: Contains positively charged protons (Z) and neutral neutrons (N).
- Nucleon/mass number (A): Sum of protons and neutrons.
- Isotopes: Atoms of the same element with different neutron numbers.
- Isotones: Atoms with the same neutron number (N).
- Isobars: Atoms with the same mass number (A).
- Nuclear stability:
- Green band in N-Z graph represents stable nuclei.
- Red band represents nuclei with excess neutrons (N/Z ratio much higher than 1), leading to β- decay and neutron transformation into a proton for stability.
- Blue strip represents nuclei with a N/Z ratio close to 1 (too many protons), leading to β+ decay and proton transformation into a neutron for stability.
- Hatched elliptical area represents heavy nuclei undergoing α decay or fission.
- Light nuclei are unable to emit α particles due to energetic constraints.
Semiempirical Model of Nuclear Binding Energy
- Model treats nucleus as an incompressible droplet.
- Weizsäcker formula calculates the binding energy based on:
- Volumetric term: Proportional to A, represents nuclear force contribution.
- Surface term: Accounts for decreased binding energy at the surface of the nucleus.
- Coulomb term: Represents the electrostatic repulsion between protons.
- Symmetry term: Accounts for the difference in energy levels between protons and neutrons due to asymmetric nucleon distribution.
Nuclear Shell Model
- Assumes that nucleons occupy discrete energy levels within the nucleus.
- Elements with "magic numbers" of protons or neutrons have many stable isotopes and are very stable.
- Based on independent shell systems for protons and neutrons.
- Predicts shells analogous to electron shells (1s, 1p, 2s, 1d, etc.).
- Limitations: Works better for lighter nuclei and doesn't accurately predict magic numbers for heavier nuclei.
- Neutron vs. proton shells remain separate.
Stability of Nuclei
- Even Z and N generally result in stable nuclei.
- N/Z ratio ≈ 1 is crucial for stability in light nuclei.
- N/Z ratio > 1 is important for stability in heavy nuclei.
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Description
This quiz examines the processes of nuclear decay, focusing on electron capture and energy quantization. It also delves into radioactive decay and the concept of half-life, covering how parent nuclei decrease over time. Test your understanding of these fundamental concepts in nuclear physics.
