Chapter 20: Problem 44
Predict the type of radioactive decay process that is likely for each of the following nuclides. a \({ }_{30}^{60} \mathrm{Zn}\) b) \({ }_{6}^{10} \mathrm{C}\) c) \({ }_{93}^{241} \mathrm{~Np}\)
Short Answer
Expert verified
Zinc-60 undergoes positron emission; Carbon-10 undergoes beta-plus decay; Neptunium-241 undergoes alpha decay.
Step by step solution
01
Understand Radioactive Decay
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A common way to predict the type of decay is to examine the neutron-to-proton (N/Z) ratio, and consider the mass number (A) and atomic number (Z). Common types of decay include alpha, beta-minus, beta-plus (positron), and electron capture.
02
Analyze the Nuclide \\(_{30}^{60} \mathrm{Zn}\\)
Zinc-60 has 30 protons and 30 neutrons (N = A - Z = 60 - 30 = 30). The neutron-to-proton ratio is 1, which is stable for lighter elements like zinc. However, Zinc-60 is rare and its decay mode tends to involve positron emission or electron capture due to proximity to stable Zinc-58.
03
Analyze the Nuclide \\(_{6}^{10} \mathrm{C}\\)
Carbon-10 has 6 protons and 4 neutrons (N = A - Z = 10 - 6 = 4). A neutron-to-proton ratio of 0.67 is too low, making it proton-rich. Such nuclides generally undergo beta-plus decay or positron emission to approach a more stable configuration.
04
Analyze the Nuclide \\(_{93}^{241} \mathrm{Np}\\)
Neptunium-241 has 93 protons and 148 neutrons (N = A - Z = 241 - 93 = 148). The neutron-to-proton ratio is 1.59, which is common for heavy, neutron-rich elements. These elements predominantly undergo alpha decay to release excess energy and protons.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Neutron-to-Proton Ratio
To predict the type of radioactive decay, it is essential to first understand the neutron-to-proton ratio (N/Z) in a nucleus. This ratio is a key indicator of stability or instability in atomic structures. A nucleus tends to be stable when this ratio is close to 1 for lighter elements. For heavier elements, stability is often achieved at a ratio slightly greater than 1.
- If the N/Z ratio is too high, the nucleus is neutron-rich and likely undergoes beta-minus decay.
- If the N/Z ratio is too low, the nucleus is proton-rich and might experience beta-plus decay or positron emission.
Alpha Decay
Alpha decay occurs when a heavy nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This process is common in elements with a high atomic number, such as those greater than lead (Pb). It helps to shed excess protons and neutrons, bringing the nucleus closer to a stable state.
- In alpha decay, the mass number decreases by 4, and the atomic number decreases by 2.
- This type of decay is energy-releasing and helps reduce the size of the large nucleus.
Beta Decay
Beta decay involves the transformation of a neutron into a proton or vice versa, resulting in the emission of beta particles. It serves to adjust the neutron-to-proton ratio towards a more stable configuration. There are two main types of beta decay: beta-minus and beta-plus (positron emission).
Beta-minus Decay
In beta-minus decay, a neutron is converted into a proton, with the release of an electron (beta particle) and an antineutrino. This form of decay is typical for neutron-rich nuclei.- Results in an increase of the atomic number by 1.
- Emits a beta particle with relatively high energy.
Beta-plus Decay (Positron Emission)
Beta-plus decay occurs when a proton is transformed into a neutron, releasing a positron and a neutrino. Positron emission is commonly found in proton-rich nuclei.- Reduces the atomic number by 1.
- Emits a positron, the antimatter counterpart of the electron.
Positron Emission
Positron emission is a fascinating process where a proton in the nucleus turns into a neutron, emitting a positron along with a neutrino. This process decreases the proton number, adjusting the neutron-to-proton ratio to stabilize the nucleus.
- Occurs in proton-rich nuclei where converting a proton to a neutron improves stability.
- The emitted positron is the antimatter equivalent of an electron, carrying a positive charge.