Question

What is the nuclear configuration of the daughter nucleus associated with the alpha decay of \(\operatorname{Hf}(A=157, Z=72) ?\)

Short answer

Answer: The nuclear configuration of the daughter nucleus is Ytterbium with mass number 153 and atomic number 70, represented as Yb(A=153, Z=70).

Step-by-step solution

Note down the initial nuclear configuration of Hafnium

The initial nuclear configuration of Hafnium is given as Hf(A=157, Z=72), meaning it has a mass number of 157 and an atomic number of 72.

Recall the composition of an alpha particle

During alpha decay, an alpha particle is emitted. An alpha particle is essentially a helium nucleus with a mass number A = 4 and an atomic number Z = 2.

Determine the nuclear configuration of the daughter nucleus after alpha decay

When an alpha particle is emitted, the mass number and atomic number of the parent nucleus decrease. To find the nuclear configuration of the daughter nucleus, we subtract the mass number and atomic number of the alpha particle from the initial nuclear configuration of the Hafnium nucleus: New A = Initial A - Alpha A = 157 - 4 = 153 New Z = Initial Z - Alpha Z = 72 - 2 = 70

Identify the element associated with the new atomic number

Now that we have the new atomic number (Z = 70), we can identify the corresponding element in the periodic table. The element with Z = 70 is Ytterbium (Yb).

Write the nuclear configuration of the daughter nucleus

The daughter nucleus has a mass number A = 153 and atomic number Z = 70, so its nuclear configuration is Yb(A=153, Z=70). The nuclear configuration of the daughter nucleus associated with the alpha decay of \(\operatorname{Hf}(A=157, Z=72)\) is \(\operatorname{Yb}(A=153, Z=70)\).

Key concepts

Nuclear Configuration

The nuclear configuration is a way to describe the nucleus of an atom, which includes how many protons and neutrons it contains.

In the context of alpha decay, it's essential to understand that this process alters the original nuclear configuration by emitting an alpha particle, which is composed of two protons and two neutrons. In other words, the mass number decreases by 4, and the atomic number decreases by 2. For example, when Hafnium undergoes alpha decay, its new nuclear configuration has 4 fewer nucleons (protons and neutrons combined) and becomes Ytterbium with 2 fewer protons.

Atomic Number

The atomic number is a fundamental property of an element that determines its position in the periodic table and its chemical characteristics. It is denoted by the symbol 'Z' and represents the number of protons in an atom's nucleus.

When an atom undergoes alpha decay, its atomic number decreases by 2 because the emitted alpha particle consists of 2 protons. This reduction in atomic number changes the element itself. For instance, Hafnium with atomic number 72 transmutes into Ytterbium, with atomic number 70, after releasing an alpha particle.

Mass Number

The mass number, represented by 'A', is the total number of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number can vary for a given element, creating different isotopes.

During alpha decay, the mass number diminishes by 4 as the atom loses an alpha particle containing 2 protons and 2 neutrons. As a result, an atom such as Hafnium (A=157) will end up with a new mass number of 153 post alpha decay, indicating a change in its nuclear configuration.

Periodic Table

The periodic table is the roadmap of elements, organized by increasing atomic number and grouped into periods and families based on similar properties. Each element's position reflects its atomic number and thus its electron configuration.

With alpha decay causing a change in atomic number by 2, the way we identify the new element resulting from this process is through the periodic table. For example, after alpha decay of Hafnium (Z=72), we locate the atomic number 70 to find Ytterbium as the resulting new element.

Nuclear Physics

Nuclear physics is the branch of physics that studies atomic nuclei and their constituents and interactions. The understanding of processes like alpha decay is a direct application of nuclear physics principles.

Through nuclear physics, we learn how unstable nuclei can transform into more stable ones by emitting particles, such as in alpha decay, which leads to a decrease in both atomic and mass numbers. This expulsion of an alpha particle can also result in a release of energy, a concept critical to power generation in nuclear reactors and the destructive power of atomic weapons.