Question

When a nucleus emits a beta particle, by how many atomic mass units does the mass of the nucleus change? By how many units does the atomic number of the nucleus change? Explain.

Short answer

When a nucleus emits a beta particle, the mass of the nucleus changes by approximately 0 atomic mass units, as both protons and neutrons have an atomic mass of about 1 atomic mass unit (amu). However, the atomic number changes by +1 for beta-minus decay (neutron converted into a proton), and by -1 for beta-plus decay (proton converted into a neutron).

Step-by-step solution

Understand beta decay

In nuclear physics, beta decay is a type of radioactive decay in which a nucleus undergoes a transformation and emits a beta particle, which can be either an electron or a positron. The two types of beta decay are: 1. Beta-minus (β-) decay: A neutron within the nucleus is converted into a proton, and an electron (beta-minus particle) is emitted. 2. Beta-plus (β+) decay: A proton within the nucleus is converted into a neutron, and a positron (beta-plus particle) is emitted.

Identify the changes in the atomic mass and atomic number for beta-minus decay

In beta-minus decay, a neutron is converted into a proton. Since both protons and neutrons have an atomic mass of approximately 1 atomic mass unit (amu), there is no significant change in the total mass of the nucleus. Therefore, the change in atomic mass units is approximately 0. However, since a neutron is converted into a proton, the atomic number (which represents the number of protons in a nucleus) increases by 1. Therefore, the change in the atomic number is +1.

Identify the changes in the atomic mass and atomic number for beta-plus decay

In beta-plus decay, a proton is converted into a neutron. Similar to beta-minus decay, since both protons and neutrons have an atomic mass of approximately 1 atomic mass unit (amu), there is no significant change in the total mass of the nucleus. Therefore, the change in atomic mass units is still approximately 0. However, since a proton is converted into a neutron, the atomic number (which represents the number of protons in a nucleus) decreases by 1. Therefore, the change in the atomic number is -1. To summarize the results: - Change in atomic mass units: 0 (approximate) for both beta-minus and beta-plus decay - Change in atomic number: +1 for beta-minus decay; -1 for beta-plus decay

Key concepts

Atomic Mass Units

Atomic mass units (amu) provide a standard to measure the mass of atoms and subatomic particles. One amu is defined as one twelfth of the mass of a carbon-12 atom. Both protons and neutrons are close in mass, approximately 1 amu. During beta decay, whether beta-minus or beta-plus, a neutron is converted to a proton or vice versa. This transformation does not significantly alter the total mass of the nucleus because the mass of a neutron and a proton are so similar.

This is why after a beta decay event, the mass of the nucleus effectively remains unchanged in terms of atomic mass units, with the change being approximately 0 amu.

Atomic Number Changes

The atomic number of an element is indicative of the number of protons in its nucleus and, thereby, its identity as a particular element. In beta-minus decay, a neutron in the nucleus is transformed into a proton causing the atomic number to increase by 1. Conversely, in beta-plus decay, a proton is converted into a neutron, which results in the decrease of the atomic number by 1.

These changes are crucial as they transform the original atom into a different element, with either one more or one less proton, signifying the transmutation of elements as a consequence of radioactive decay.

Nuclear Physics

Nuclear physics is the branch of physics that studies the constituents and interactions of atomic nuclei. Fundamental to our understanding of the elements, nuclear physics explains phenomena such as radioactive decay and nuclear reactions. Beta decay is one such phenomenon, where nuclear forces within the atom's nucleus change one type of subatomic particle into another, emitting particles and radiation in the process.

This transformation results in a reconfiguration of the nucleus's inhabitants—the protons and neutrons—which can alter the element itself. Understanding beta decay requires a grasp of the delicate balance of forces at play within the nucleus.

Radioactive Decay

Radioactive decay is a spontaneous process by which the nucleus of an unstable atom loses energy. This can occur in several ways: alpha decay, beta decay, or gamma decay, among others. Beta decay, specifically, entails the release of beta particles—a term which encompasses both electrons (in beta-minus decay) and positrons (beta-plus decay).

During radioactive decay, the atoms undergo a transformation in terms of their identity (changing elements) and stability (releasing excess energy). This process is natural and continuous, playing a vital role in many fields, from medicine to energy production.

Beta Particle Emission

Beta particle emission is at the heart of beta decay. In beta-minus decay, an electron is emitted when a neutron turns into a proton. In contrast, during beta-plus decay, a positron (the antimatter counterpart of an electron) is released as a proton is converted into a neutron. These particles, beta-minus and beta-plus, carry away excess energy in the form of kinetic energy, which is detected as radiation.

While the mass and atomic number of the nucleus are affected, as previously explained, the total charge of the nucleus is preserved, as beta particles are charged particles that effectively balance the nuclear charge change.