Chapter 21: Problem 15
Decay of which nucleus will lead to the following products: \((\mathbf{a})\) uranium- 235 by alpha decay; (b) aluminium-26 by positron emission; (c) deuterium by alpha decay; (d) yttrium-90 by beta decay?
Short Answer
Expert verified
(a) Thorium-231; (b) Magnesium-26; (c) None; (d) Zirconium-90.
Step by step solution
01
Understanding Alpha Decay
Alpha decay involves the loss of an alpha particle from a nucleus, which consists of 2 protons and 2 neutrons. This decreases the atomic number by 2 and the mass number by 4.
02
Uranium-235 by Alpha Decay
Uranium-235 (\(_{92}^{235}U\)) undergoes alpha decay, reducing the atomic number to 90 and the mass number to 231. The resulting nucleus is thorium-231 (\(_{90}^{231}Th\)).
03
Understanding Positron Emission
Positron emission is a type of beta decay where a proton in the nucleus is converted into a neutron, releasing a positron. This decreases the atomic number by 1 while keeping the mass number constant.
04
Aluminium-26 by Positron Emission
When aluminium-26 (\(_{13}^{26}Al\)) undergoes positron emission, its atomic number decreases to 12, leading to the formation of magnesium-26 (\(_{12}^{26}Mg\)).
05
Verifying Deuterium by Alpha Decay
Deuterium (\(_{1}^{2}H\)) cannot undergo alpha decay because it lacks enough nucleons to emit an alpha particle, which requires at least 4 nucleons. Thus, no valid decay product exists for deuterium by alpha decay.
06
Understanding Beta Decay
Beta decay involves the conversion of a neutron to a proton, or vice versa, changing the atomic number by 1 in either direction without altering the mass number.
07
Yttrium-90 by Beta Decay
Yttrium-90 (\(_{39}^{90}Y\)) undergoes beta decay, increasing the atomic number to 40 and forming zirconium-90 (\(_{40}^{90}Zr\)).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Alpha Decay
Alpha decay is a type of radioactive decay where an unstable nucleus ejects an alpha particle. An alpha particle is essentially a helium nucleus, composed of 2 protons and 2 neutrons. This process decreases the atomic number by 2 and the mass number by 4, effectively transforming the original element into a different one.
For instance, when uranium-235 undergoes alpha decay, it transforms into thorium-231.
In general, not all nuclei can undergo alpha decay. Deuterium, for example, only has 2 nucleons in total, making it impossible to emit an alpha particle.
For instance, when uranium-235 undergoes alpha decay, it transforms into thorium-231.
- The atomic number of uranium is 92, but after losing 2 protons, it becomes 90, which is the atomic number of thorium.
- The mass number reduces from 235 to 231, as the 4 nucleons making up the alpha particle are no longer part of the nucleus.
In general, not all nuclei can undergo alpha decay. Deuterium, for example, only has 2 nucleons in total, making it impossible to emit an alpha particle.
Positron Emission
Positron emission, also known as beta-plus decay, is a unique type of radioactive decay. It involves the conversion of a proton within the nucleus into a neutron. During this transformation, a positron and a neutrino are emitted from the nucleus.
This leads to a decrease in the atomic number by 1, but the mass number remains unchanged.
When aluminium-26 undergoes positron emission, it forms magnesium-26.
This decay process helps the atom reach a more stable state by altering its internal composition.
This leads to a decrease in the atomic number by 1, but the mass number remains unchanged.
When aluminium-26 undergoes positron emission, it forms magnesium-26.
- This is because the atomic number drops from 13 (aluminium) to 12 (magnesium).
- The mass number stays at 26, as the overall number of nucleons remains constant.
This decay process helps the atom reach a more stable state by altering its internal composition.
Beta Decay
Beta decay is a process that enables unstable nuclei to achieve greater stability. It involves two primary types: beta-minus decay and beta-plus decay. We have already discussed positron emission as beta-plus decay.
In beta-minus decay, a neutron is converted into a proton within the nucleus. During this conversion, an electron (known as a beta particle) and an antineutrino are emitted. Consequently, the atomic number increases by 1, while the mass number remains constant.
In beta-minus decay, a neutron is converted into a proton within the nucleus. During this conversion, an electron (known as a beta particle) and an antineutrino are emitted. Consequently, the atomic number increases by 1, while the mass number remains constant.
- An example of this process is the decay of yttrium-90 to zirconium-90.
- The atomic number of yttrium increases from 39 to 40, transforming it into zirconium.
- The mass number stays at 90 because the total number of nucleons remains the same.