Chapter 21: Problem 17
Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{5}^{8} \mathrm{~B},\) (b) \({ }_{29}^{68} \mathrm{Cu},\) (c) phosphorus-32, (d) chlorine- 39 .
Short Answer
Expert verified
(a) Beryllium-8: Beta-plus decay
(b) Copper-68: Electron capture or beta-plus decay
(c) Phosphorus-32: Beta-minus decay
(d) Chlorine-39: Beta-minus decay
Step by step solution
01
Identify the radionuclide
Determine the element, atomic number (Z), and mass number (A) for the radionuclide in question.
(a) Beryllium-8: Element: Beryllium (Be); Z: 5; A: 8
(b) Copper-68: Element: Copper (Cu); Z: 29; A: 68
(c) Phosphorus-32: Element: Phosphorus (P); Z: 15; A: 32
(d) Chlorine-39: Element: Chlorine (Cl); Z: 17; A: 39
02
Calculate Neutron-to-Proton ratio (N/P)
Calculate the Neutron-to-Proton ratio for each radionuclide using the formula N/P = (A - Z) / Z.
(a) Beryllium-8: N/P = (8 - 5) / 5 = 0.6
(b) Copper-68: N/P = (68 - 29) / 29 = 1.34
(c) Phosphorus -32: N/P = (32 - 15) / 15 = 1.13
(d) Chlorine-39: N/P = (39 - 17) / 17 = 1.29
03
Evaluate Stable N/P Range
Compare the calculated N/P ratio with the stable N/P range for each element to predict the type of radioactive decay process.
(a) Beryllium-8: The stable N/P range for light elements (Z < 20) is typically N/P ≈ 1. Since 0.6 < 1, it will likely undergo a beta-plus decay to increase Z.
(b) Copper-68: The stable N/P range for intermediate elements (20 < Z < 80) is typically N/P ≈ 1.25-1.5. Since 1.34 is within this range, copper-68 possibly undergoes electron capture or a beta-plus decay.
(c) Phosphorus -32: The stable N/P range for light elements (Z < 20) is typically N/P ≈ 1. Since 1.13 > 1, it will likely undergo a beta-minus decay to decrease Z.
(d) Chlorine-39: The stable N/P range for light elements (Z < 20) is typically N/P ≈ 1. Since 1.29 > 1, it will likely undergo a beta-minus decay to decrease Z.
04
Final Predicted Decay Types
Based on the comparisons in Step 3, we predict the following decay types for each radionuclide:
(a) Beryllium-8: Beta-plus decay
(b) Copper-68: Electron capture or beta-plus decay
(c) Phosphorus-32: Beta-minus decay
(d) Chlorine-39: Beta-minus decay
Hence, we have predicted the decay types for each of the given radionuclides using their neutron-to-proton ratios and stable N/P ranges for their respective elements.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Neutron-to-Proton Ratio
Understanding the neutron-to-proton (N/P) ratio in atomic nuclei is essential for predicting radioactive decay types. It helps us determine the stability of an isotope and foresee which radioactive decay process might occur if the isotope is unstable.
In stable atoms, the N/P ratio is balanced, meaning there's a certain equilibrium between the number of neutrons and protons. For lighter elements (with atomic numbers less than 20), the ratio is typically close to 1:1. As we move towards heavier elements, the ratio gradually increases to accommodate additional neutrons required for stabilizing the nucleus against the increasing proton-proton repulsive forces.
When the N/P ratio is too low, it means there are too many protons in the nucleus, and the atom might undergo beta-plus decay (positron emission) or electron capture to convert a proton into a neutron, thereby increasing the N/P ratio towards stability. Conversely, when the N/P ratio is too high, indicating an excess of neutrons, the nucleus might experience beta-minus decay (electron emission), where a neutron converts into a proton.
For instance, if we examine Beryllium-8, with an N/P ratio of 0.6 (significantly less than 1), it is predicted to undergo beta-plus decay to address this imbalance. This simple yet powerful prediction tool hinges on the fundamental understanding of the delicate balance needed within the atomic nucleus.
In stable atoms, the N/P ratio is balanced, meaning there's a certain equilibrium between the number of neutrons and protons. For lighter elements (with atomic numbers less than 20), the ratio is typically close to 1:1. As we move towards heavier elements, the ratio gradually increases to accommodate additional neutrons required for stabilizing the nucleus against the increasing proton-proton repulsive forces.
When the N/P ratio is too low, it means there are too many protons in the nucleus, and the atom might undergo beta-plus decay (positron emission) or electron capture to convert a proton into a neutron, thereby increasing the N/P ratio towards stability. Conversely, when the N/P ratio is too high, indicating an excess of neutrons, the nucleus might experience beta-minus decay (electron emission), where a neutron converts into a proton.
For instance, if we examine Beryllium-8, with an N/P ratio of 0.6 (significantly less than 1), it is predicted to undergo beta-plus decay to address this imbalance. This simple yet powerful prediction tool hinges on the fundamental understanding of the delicate balance needed within the atomic nucleus.
Beta Decay
Beta decay represents a fundamental process by which unstable nuclei achieve greater stability. It plays a pivotal role in the transformation of a radionuclide and involves the emission of beta particles, which can be either electrons or positrons, depending on the type of decay.
Consider beta-minus decay: when a nucleus has an excessive number of neutrons, as calculated by comparing the N/P ratio to the known stable ranges, one of these neutrons is transformed into a proton, an electron (the beta particle), and an antineutrino. The emitted electron is ejected from the nucleus, hence the term 'decay'. In the case of Phosphorus-32, with an N/P ratio of 1.13, beta-minus decay will likely occur to decrease its atomic number, thus reducing the N/P ratio towards the stable range.
Beta-plus decay operates on the inverse premise – here, an excess proton is converted into a neutron, a positron (the beta particle), and a neutrino. For Beryllium-8 and its low N/P ratio of 0.6, a positron emission is likely to happen to increase the N/P ratio and stabilize the nucleus. This transformation leads to an interesting phenomenon where the identity of the element changes because the atomic number, which determines the element, has altered.
Consider beta-minus decay: when a nucleus has an excessive number of neutrons, as calculated by comparing the N/P ratio to the known stable ranges, one of these neutrons is transformed into a proton, an electron (the beta particle), and an antineutrino. The emitted electron is ejected from the nucleus, hence the term 'decay'. In the case of Phosphorus-32, with an N/P ratio of 1.13, beta-minus decay will likely occur to decrease its atomic number, thus reducing the N/P ratio towards the stable range.
Beta-plus decay operates on the inverse premise – here, an excess proton is converted into a neutron, a positron (the beta particle), and a neutrino. For Beryllium-8 and its low N/P ratio of 0.6, a positron emission is likely to happen to increase the N/P ratio and stabilize the nucleus. This transformation leads to an interesting phenomenon where the identity of the element changes because the atomic number, which determines the element, has altered.
- Beta-minus decay: Increases atomic number.
- Beta-plus decay: Decreases atomic number.
Electron Capture
Electron capture is another process for atomic nuclei to move toward stability, especially when there's a surplus of protons. Unlike beta decay, where particles are emitted from the nucleus, electron capture involves an inner orbital electron being pulled into the nucleus.
During this process, one of the nucleus's protons captures a nearby orbital electron and turns into a neutron, releasing a neutrino. This does not result in an emission of particles outside the nucleus, thus distinguishing it from beta decay. Instead, the captured electron neutralizes one of the protons, reducing the atom's atomic number by one.
Taking Copper-68 as an example, with an N/P ratio of 1.34 – comfortably within the predicted stable range for heavier elements – we might expect an electron capture to occur. Not only does this process stabilize the nucleus by adjusting the N/P ratio, but it's also noteworthy that electron capture is often accompanied by a characteristic X-ray, which occurs when the electron shells rearrange themselves following the capture.
Since electron capture often competes with beta-plus decay as a mode of decay for proton-rich nuclei, its prediction requires careful consideration of energy levels and the internal electron arrangements of the atom.
During this process, one of the nucleus's protons captures a nearby orbital electron and turns into a neutron, releasing a neutrino. This does not result in an emission of particles outside the nucleus, thus distinguishing it from beta decay. Instead, the captured electron neutralizes one of the protons, reducing the atom's atomic number by one.
Taking Copper-68 as an example, with an N/P ratio of 1.34 – comfortably within the predicted stable range for heavier elements – we might expect an electron capture to occur. Not only does this process stabilize the nucleus by adjusting the N/P ratio, but it's also noteworthy that electron capture is often accompanied by a characteristic X-ray, which occurs when the electron shells rearrange themselves following the capture.
Since electron capture often competes with beta-plus decay as a mode of decay for proton-rich nuclei, its prediction requires careful consideration of energy levels and the internal electron arrangements of the atom.
