Question

When a nucleus emits a neutron, does the atomic number of the nucleus change? Does the mass number of the nucleus change? Explain.

Short answer

When a nucleus emits a neutron, the atomic number (Z) of the nucleus does not change because the number of protons remains the same. However, the mass number (A) of the nucleus does change, as the total number of nucleons (protons and neutrons) decreases by one due to the loss of a neutron. Thus, $A^{\prime }=A-1$.

Step-by-step solution

Define Atomic Number and Mass Number

The atomic number (Z) is the number of protons in the nucleus of an atom. The atomic number defines the element it represents and also determines its chemical properties. The mass number (A) is the total number of protons and neutrons in the nucleus of an atom.

Nuclear Reaction when a Neutron is Emitted

When a nucleus emits a neutron, it experiences a change in its neutron number, but not the number of protons. The nucleus goes from an initial state $X(A,Z)$ to a final state $Y(A^{\prime },Z^{\prime })$, where A and Z represent the initial mass number and atomic number, respectively, and A' and Z' represent the final mass number and atomic number.

Determine Changes in Atomic Number and Mass Number

Since the number of protons in the nucleus remains unchanged during the emission of a neutron, the atomic number remains the same. That is, $Z=Z^{\prime }$. The mass number, however, is the total number of protons and neutrons in the nucleus. Since a neutron is being emitted, the total number of nucleons (protons and neutrons) decreases by one. Therefore, $A^{\prime }=A-1$.

Conclusion

When a nucleus emits a neutron, the atomic number (Z) of the nucleus does not change, as there is no change in the number of protons. However, the mass number (A) of the nucleus does change, as the total number of nucleons decreases by one due to the loss of a neutron.

Key concepts

Atomic Number

The atomic number, often symbolized by the letter **Z**, represents the number of protons in the nucleus of an atom. It plays a crucial role in defining the identity of an element on the periodic table.
Each element is uniquely associated with a specific atomic number. For example, the element hydrogen has an atomic number of 1, meaning it has one proton in its nucleus, while helium has an atomic number of 2, indicating two protons.

• The atomic number is essential as it determines the chemical properties and behavior of the element.
• It is a constant for any given element; thus, changes to the atomic number signify transformation into a different element.

In the context of nuclear reactions, such as when a neutron is emitted, the atomic number remains unchanged. This is because the emission of a neutron does not alter the number of protons within the nucleus. Therefore, the identity of the element remains the same, ensuring the atomic number stays constant.

Mass Number

The mass number, symbolized by the letter **A**, is the sum of the protons and neutrons in the nucleus of an atom. Unlike the atomic number, the mass number is not constant across all atoms of an element because isotopes of elements have different neutron counts.

• For example, carbon typically has a mass number of 12, including 6 protons and 6 neutrons, but its isotope Carbon-14 has 8 neutrons, changing its mass number to 14.
• In nuclear reactions, the mass number reflects the entire collection of nucleons (protons and neutrons).

When a neutron is emitted from the nucleus during a nuclear reaction, the mass number decreases by one. This is because one less neutron results in the reduction of the total nucleon count by one, changing the mass number without affecting the atomic number.
Thus, in such a nuclear event, if the initial nucleus is represented by $X(A,Z)$, the resulting nucleus has a mass number $A^{\prime }=A-1$, while the atomic number $Z$ remains unchanged.

Nucleus Emission

Nucleus emission refers to the process where particles such as neutrons, protons, or alpha particles are emitted from a nucleus.
This is a common occurrence in radioactive decay and certain nuclear reactions.

• This emission can significantly impact the stability and identity of a nucleus.
• Different types of emissions cause distinct changes in the nucleus's structure and composition.

In situations where a neutron is emitted:

• The atomic number, $Z$, remains unchanged since the number of protons does not vary.
• The mass number, $A$, decreases by one because of the loss of the neutron, which is a part of the nucleon count.

Apart from changing mass numbers, such emissions can also lead to transformations into different isotopes, potentially altering the physical and chemical behavior of the element. Understanding nucleus emission is essential for grasping concepts in nuclear physics, such as radioactive decay and stability of nuclides.