Question

During the transformation of \(\mathrm{X}^{\mathrm{b}} \longrightarrow \mathrm{C}^{\mathrm{d}}\) the number of \(\beta\) particles emitted is (a) \(\frac{(b-d)}{4}\) (b) \((c-a)+1 / 2(b-d)\) (c) \((a-c)-1 / 2(b-d)\) (d) \((b-d)+2(c-a)\)

Short answer

(b-d)+2(c-a) is the correct option.

Step-by-step solution

Understanding the Problem

We need to figure out the number of \(\beta\) particles emitted during the transformation \(X^b \rightarrow C^d\). The given choices involve mathematical expressions based on \(a, b, c,\) and \(d\).

Analyzing \(\beta\) Decay

In a \(\beta\) decay process, a neutron in the nucleus decays into a proton, and an electron (the \(\beta\) particle) and an antineutrino are emitted. This increases the atomic number by 1 while the mass number remains unchanged.

Applying Nuclear Change

The transformation \(X^b \rightarrow C^d\) implies a change in atomic number from \(b\) to \(d\), suggesting \(d - b\) \(\beta\) particles are emitted because each \(\beta\) particle increases the atomic number by 1.

Identifying the Correct Option

Looking at the choices, the expression \((b-d)\) corresponds to the correct transformation of \(b\) turning into \(d\), however, the presence of other terms in the choices must be considered. The appropriate choice should simplify to this basic transformation without extra terms related to mass number or other elements.

Analyzing Each Choice

- (a) \(\frac{(b-d)}{4}\) suggests a fraction which does not match our understanding of whole emissions.- (b) \((c-a)+1 / 2(b-d)\) involves a mass change, irrelevant for \(\beta\) decay.- (c) \((a-c)-1 / 2(b-d)\) similarly combines mass-related information.- (d) \((b-d)+2(c-a)\) distills to the \((b-d)\) part we need, but without inappropriate fractions or adjustments.

Selecting the Correct Choice

The option (d) \((b-d)+2(c-a)\) checks out, considering it closely aligns with the necessary transformation in atomic number while potentially accounting for unseen offsets without affecting pure \(b-d\) change logic from neutron to proton-caused emissions.

Key concepts

Nuclear Chemistry

Nuclear chemistry is a fascinating branch of science that explores reactions at the atomic level, particularly within atomic nuclei. Unlike typical chemistry that involves the study of electron interactions and chemical bonds, nuclear chemistry focuses on changes in the nuclei of atoms. This often involves the transformation of one element into another.

One of the essential processes studied in nuclear chemistry is radioactive decay, which includes types such as alpha, beta, and gamma decay. During these decays, particles are emitted which leads to the transformation of the original element into a different element or isotope. The energy released during these reactions is usually significant and can be harnessed for various applications, from nuclear power to medical treatments.

Understanding nuclear chemistry is crucial not only for scientific exploration but also for its applications in energy production and its implications for safety in nuclear technology.

Atomic Number

The atomic number of an element is the unique identifier representing the number of protons within the nucleus of an atom of that element. This number defines the chemical properties of the element and its position in the periodic table. Each element has a distinct atomic number, starting from hydrogen with an atomic number of 1.

In nuclear reactions, the atomic number is very important because it determines the identity of the element. For instance, during beta decay, the atomic number of an element increases by one as a neutron in the nucleus is transformed into a proton. Despite these changes, the mass number, which is the total number of protons and neutrons, remains constant.

Understanding the changes in atomic numbers is crucial when dealing with nuclear reactions or particle emissions, as it helps to correctly identify the resultant particles and new elements formed.

Particle Emissions

Particle emissions are a key concept in understanding nuclear reactions. They occur when unstable nuclei release particles to achieve a more stable state. During these emissions, particles such as alpha particles, beta particles, and gamma rays are released.

In beta decay, for example, a beta particle, which is essentially a high-energy electron, is emitted from the nucleus. This happens when a neutron in the nucleus transforms into a proton, increasing the atomic number by one, resulting in a new element. Unlike alpha particles that consist of two protons and two neutrons, beta particles have no mass number change because the proton number increase is balanced by the neutron transformation.

Understanding these emissions helps us comprehend how elements transform and also provides insight into the energy release during nuclear reactions.

Nuclear Reactions

Nuclear reactions involve changes to an atom's nucleus and can lead to the transformation of elements. These reactions often release or absorb a large amount of energy, much greater than in typical chemical reactions.

Types of nuclear reactions include fission, where a nucleus splits into smaller parts, and fusion, where smaller nuclei combine to form a larger nucleus. Another common type is radioactive decay, which includes processes like beta decay. In beta decay, the atomic number of an atom increases when a neutron turns into a proton, emitting a beta particle.

Understanding nuclear reactions is critical as they underpin technologies in energy production and medical applications, and thankfully, also informs safety practices in handling radioactive materials. These reactions not only help us in technological advancements but also reveal the inner workings of atomic processes in the universe.