Question

Complete the following nuclear reaction: \({ }_{25} \mathrm{Mn}^{55}(n, \gamma)\) (a) \({ }_{25} \mathrm{Mn}^{55}\) (b) \({ }_{24} \mathrm{Cr}^{56}\) (c) \({ }_{24} \mathrm{Cr}^{54}\) (d) \({ }_{25} \mathrm{Mn}^{56}\)

Short answer

The complete nuclear reaction is \( {}_{25}Mn^{55}(n, \gamma) \rightarrow {}_{25}Mn^{56} \) which corresponds to option (d).

Step-by-step solution

Understanding the Nuclear Reaction

Begin by understanding the given nuclear reaction notation. A reaction of the form \( {}_{Z}X^{A}(n,\gamma) \) represents the absorption of a neutron (n) and the emission of a gamma photon (\gamma) by the nucleus X, where Z is the atomic number (number of protons) and A is the mass number (number of protons plus neutrons). The question requires us to find the resulting nuclide after this process.

Determine the Resulting Isotope

The absorption of a neutron will increase the mass number (A) of the nucleus by 1 while keeping the atomic number (Z) unchanged (since neutron carries no charge). Since the starting element is \( {}_{25}Mn^{55} \) and the process involves absorbing one neutron, the resulting isotope will have a mass number of 55 + 1 = 56 and an atomic number of 25 (unchanged).

Identify the Correct Result

Since the atomic number remains at 25 and the mass number increased to 56, the correct resulting isotopic symbol after the nuclear reaction is \( {}_{25}Mn^{56} \) which corresponds to option (d).

Key concepts

Neutron Absorption

Neutron absorption is a type of nuclear reaction that occurs when a neutron is captured by the nucleus of an atom. This process is significant in both natural and artificial nuclear reactions. When a neutron is absorbed by a nucleus, the mass number (A), which represents the total number of protons and neutrons in the nucleus, increases by one because a neutron has been added to the nucleus. However, the atomic number (Z), which is the number of protons and hence defines the chemical element, remains unchanged.

In nuclear reactors, neutron absorption is a critical process. It can lead to the formation of new isotopes, which can have different properties from the original atom. Understanding this concept is vital in nuclear chemistry, particularly in the fields of nuclear energy and radioactive decay.

Gamma Emission

Gamma emission refers to the process wherein an unstable nucleus releases energy in the form of gamma rays, a type of high-energy electromagnetic radiation. This process often follows nuclear reactions such as neutron absorption, where the capture of a neutron can leave a nucleus in an excited energy state.

To return to a stable state, the nucleus emits this excess energy as gamma radiation, which contains no charge and does not alter the number of protons or neutrons in the nucleus. Gamma rays are highly penetrating and can be hazardous due to their ability to ionize atoms and molecules in their path. In the context of nuclear reactions, gamma emission is represented by the symbol \(\gamma\), which indicates that the reaction products include this type of radiation.

Isotopes Identification

Isotopes are atoms of the same element that have different numbers of neutrons but the same number of protons. This difference in neutron number gives each isotope a different mass number, although the atomic number remains the same. Identifying isotopes is fundamental in understanding nuclear reactions and their applications, such as medical diagnostics, where specific isotopes are used for imaging and treatment.

Each isotope is denoted by its chemical symbol, along with its atomic number (Z) as a subscript and its mass number (A) as a superscript. Identifying isotopes after nuclear reactions, such as neutron absorption, requires knowledge of these notations and understanding that only the mass number changes as a result of the nuclear process.

Mass Number Calculation

The mass number (A) is a critical value in nuclear chemistry that indicates the total number of protons and neutrons within an atom's nucleus. Calculating the mass number is a straightforward process; it is merely the sum of the number of protons (atomic number, Z) and the number of neutrons (N). This calculation plays a crucial role when examining nuclear reactions, specifically when identifying the products of such reactions.

For example, when an atom undergoes neutron absorption, the mass number increases by one without changing the atomic number. Understandably, the ability to calculate the new mass number is essential for correctly identifying the resulting isotope after neutron capture, as seen in the given exercise where we find the mass number increasing from 55 to 56 after the absorption of a neutron.