Understanding Beta Decay and Nuclear Changes

When a nucleus undergoes beta decay, it emits a beta ray, which is essentially a high-energy electron (β^-) or positron (β⁺). This process involves the transformation of a neutron into a proton (in β^- decay) or a proton into a neutron (in β⁺ decay) within the nucleus. These nuclear transformations cause changes in the composition of the nucleus.

Let's look at the two main types of beta decay:

• Beta-minus (β^-) Decay: In this type of beta decay, a neutron inside the nucleus decays into a proton, an electron (the β^- particle), and an electron antineutrino. $$n \rightarrow p + e^{-} + \bar{\nu}_e$$ Consider a nucleus $_Z^A X$. After emitting a β^- ray, a neutron ($N$) becomes a proton ($Z+1$), while the total number of nucleons ($A$) remains the same. The transformation is: $$_Z^A X \rightarrow _{Z+1}^A Y + e^{-} + \bar{\nu}_e$$ The proton number (atomic number, $Z$) increases by 1. The neutron number ($N = A - Z$) decreases by 1. The sum of proton and neutron numbers (mass number, $A$) remains unchanged.
• Beta-plus (β⁺) Decay: In this type of beta decay, a proton inside the nucleus decays into a neutron, a positron (the β⁺ particle), and an electron neutrino. $$p \rightarrow n + e^{+} + \nu_e$$ Consider a nucleus $_Z^A X$. After emitting a β⁺ ray, a proton ($Z$) becomes a neutron ($N+1$), while the total number of nucleons ($A$) remains the same. The transformation is: $$_Z^A X \rightarrow _{Z-1}^A Y + e^{+} + \nu_e$$ The proton number (atomic number, $Z$) decreases by 1. The neutron number ($N = A - Z$) increases by 1. The sum of proton and neutron numbers (mass number, $A$) remains unchanged.

Analyzing Changes in Nuclear Properties

Based on the types of beta decay, we can see how the different properties of the nucleus change:

The question asks what does not change when a nucleus emits a beta ray. Looking at the table and the processes described:

• The proton number (atomic number) changes in both β^- and β⁺ decay.
• The neutron number changes in both types of beta decay.
• The total charge of the nucleus (which is determined by the number of protons) changes.
• The sum of proton and neutron numbers, which is the mass number ($A$), remains constant in both β^- and β⁺ decay. This is because a nucleon is simply converting from one type (proton or neutron) to the other, keeping the total count the same.

Why the Sum of Proton and Neutron Numbers is Unchanged During Beta Ray Emission

The sum of proton and neutron numbers is the mass number ($A$). In beta decay, a neutron transforms into a proton or vice versa. One nucleon changes its identity but remains within the nucleus (or rather, one nucleon is removed and replaced by another type, keeping the total number constant). Therefore, the total number of nucleons, which is the mass number, does not change during beta decay. When a nucleus emits a beta ray, this fundamental quantity remains constant.

Thus, when a nucleus emits a beta ray, the quantity that does not change is the sum of proton and neutron numbers.