Problem 21
Question
What decay particle is emitted from a nucleus of low to intermediate atomic number but a relatively high neutron/proton ratio? How does the emission of this particle benefit the nucleus?
Step-by-Step Solution
Verified Answer
The emitted decay particle is a beta-minus (β-) particle from a nucleus with low to intermediate atomic number and high neutron/proton ratio. This emission helps stabilize the nucleus by reducing the neutron/proton ratio.
1Step 1: Identifying the Decay Particle
For a nucleus with low to intermediate atomic number but a relatively high neutron/proton ratio, the decay particle that is typically emitted is a beta particle, specifically a beta-minus (β-) particle. This occurs during beta decay, where a neutron is transformed into a proton with the emission of an electron (the beta particle) and an antineutrino.
2Step 2: Benefits to the Nucleus from Particle Emission
The emission of a beta particle (electron) benefits the nucleus by reducing the neutron to proton ratio. Since the neutron is converted into a proton, it helps stabilize the nucleus. Nuclei with high neutron/proton ratios are generally unstable, and beta decay is one of the ways the nucleus can move closer to the region of stability as defined by the band of stability on the chart of nuclides.
Key Concepts
Neutron/Proton RatioNuclear StabilityBand of Stability
Neutron/Proton Ratio
Understanding the neutron/proton ratio is crucial when studying the atomic nucleus. Elements on the periodic table consist of atoms, and each atom has a nucleus made up of neutrons and protons. The number of protons determines the element type, while the number of neutrons can vary, resulting in different isotopes of the same element.
The neutron/proton ratio is the count of neutrons to protons in an isotope's nucleus. This ratio is important because it influences the stability of the nucleus. A balanced neutron/proton ratio contributes to a stable isotope, while an imbalance can lead to radioactivity and decay. For light elements (those with a low atomic number), the ideal ratio is close to 1:1, meaning an equal number of neutrons and protons.
As elements get heavier, they require more neutrons than protons to help offset the repulsive forces between the positively charged protons. This ensures the nucleus remains compact and stable. However, once the neutron/proton ratio goes too high, the nucleus can become unstable. In such cases, a common pathway to stability is through the process of beta decay.
The neutron/proton ratio is the count of neutrons to protons in an isotope's nucleus. This ratio is important because it influences the stability of the nucleus. A balanced neutron/proton ratio contributes to a stable isotope, while an imbalance can lead to radioactivity and decay. For light elements (those with a low atomic number), the ideal ratio is close to 1:1, meaning an equal number of neutrons and protons.
As elements get heavier, they require more neutrons than protons to help offset the repulsive forces between the positively charged protons. This ensures the nucleus remains compact and stable. However, once the neutron/proton ratio goes too high, the nucleus can become unstable. In such cases, a common pathway to stability is through the process of beta decay.
Nuclear Stability
Nuclear stability refers to how well an atomic nucleus holds together. A stable nucleus has the right balance of neutrons to protons, which allows it to exist indefinitely without changing its state. Unstable nuclei, on the other hand, have an unbalanced neutron/proton ratio and tend to undergo radioactive decay to achieve stability.
There are multiple types of radioactive decay, including alpha, beta, and gamma decay. In beta decay, specifically beta-minus decay, a neutron is converted into a proton, and this process emits a beta particle (electron) along with an antineutrino.
The emission of the beta particle is crucial because it increases the number of protons while decreasing the number of neutrons, thus moving the neutron/proton ratio towards a value that favors stability. This transformation is essential for a nucleus with a high neutron/proton ratio, as it allows the element to achieve greater stability by adjusting the imbalance. Ultimately, nuclear stability is a key factor in determining the lifespan of an isotope and its behavior in nature or in applications like nuclear medicine and energy.
There are multiple types of radioactive decay, including alpha, beta, and gamma decay. In beta decay, specifically beta-minus decay, a neutron is converted into a proton, and this process emits a beta particle (electron) along with an antineutrino.
The emission of the beta particle is crucial because it increases the number of protons while decreasing the number of neutrons, thus moving the neutron/proton ratio towards a value that favors stability. This transformation is essential for a nucleus with a high neutron/proton ratio, as it allows the element to achieve greater stability by adjusting the imbalance. Ultimately, nuclear stability is a key factor in determining the lifespan of an isotope and its behavior in nature or in applications like nuclear medicine and energy.
Band of Stability
The band of stability is a visual representation on a chart of nuclides that identifies the stable combination of neutron/proton ratios for atomic nuclei. It is essentially a region on the graph where the stable isotopes reside. As isotopes have varying numbers of neutrons, this band shows which combinations do not lead to radioactive decay.
When visualizing the chart of nuclides, the x-axis typically represents proton number (atomic number), and the y-axis represents neutron number. The stable isotopes plot along a curve known as the band of stability. Isotopes that lie within this band have a stable configuration and do not undergo radioactive decay over time. Isotopes above or below the band have too many neutrons or protons, respectively, and are unstable.
Beta decay is a mechanism that enables isotopes outside the band to move towards stability. When a neutron-rich isotope, lying above the band, undergoes beta decay, it moves closer to the band, as the neutron/proton ratio is adjusted. The band of stability provides a roadmap for predicting whether a nucleus will be stable or if it might undergo decay to seek a more stable state.
When visualizing the chart of nuclides, the x-axis typically represents proton number (atomic number), and the y-axis represents neutron number. The stable isotopes plot along a curve known as the band of stability. Isotopes that lie within this band have a stable configuration and do not undergo radioactive decay over time. Isotopes above or below the band have too many neutrons or protons, respectively, and are unstable.
Beta decay is a mechanism that enables isotopes outside the band to move towards stability. When a neutron-rich isotope, lying above the band, undergoes beta decay, it moves closer to the band, as the neutron/proton ratio is adjusted. The band of stability provides a roadmap for predicting whether a nucleus will be stable or if it might undergo decay to seek a more stable state.
Other exercises in this chapter
Problem 17
Lanthanum-139 is a stable nuclide but lanthanum-140 is unstable \(\left(t_{1 / 2}=40 \mathrm{hr}\right)\). What rule of thumb concerning nuclear stability is in
View solution Problem 18
As the atomic number increases, the neutron/proton ratio increases. What does this suggest is a factor in nuclear stability?
View solution Problem 22
What decay particle is emitted from a nucleus of low to intermediate atomic number but a relatively low neutron/proton ratio? How does the emission of this part
View solution Problem 26
Rutherford theorized that a compound nucleus forms when helium nuclei hit nitrogen- 14 nuclei. If this compound nucleus decayed by the loss of a neutron instead
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