What is the change in the nucleus that results from the following decay scenarios? (a) emission of a \(\beta\) particle (b) emission of a \(\beta^{+}\) particle (c) capture of an electron

Imagine a tiny, crowded city where residents can change roles—a neutron transforms into a proton. This is similar to what happens in beta minus decay. It's a process where an unstable atomic nucleus releases a beta particle, which is essentially an electron. As one of the neutrons in the nucleus turns into a proton, it's like a resident changing jobs, altering the very identity of the atom. The atomic number, which is the count of protons, goes up by one, but the mass number—the total count of protons and neutrons—stays the same, as the transformation doesn’t add any new particles to the city, it just changes one kind into another. Imagine placing a tiny plus sign next to the atomic number, symbolizing this increase. Thanks to this process, we get a whole new element on the periodic table.

Now, let's flip the scenario. In beta plus decay, it's as if a neutron wants to move out, but instead a proton leaves, and this exodus is marked by the release of a positron, the electron's positive twin. The proton is transforming into a neutron, so the city's population remains consistent, but the roster of jobs changes—the atomic number decreases by one as the proton tally goes down. Despite this, the city’s mass stays the same because it's more about the number of houses (mass number) rather than who lives in them (protons and neutrons). It's like rewriting the address book of the atomic city, as the element steps back to its previous neighbor on the periodic lineup.

Electron capture is another intriguing event: it's when an atom's nucleus snatches an electron from its own surrounding cloud, usually the innermost shell. This captured electron merges with a proton and they transform into a neutron. It's like an official in the atomic city deciding to become a regular citizen. The process decreases the atomic number by one, but the overall size of the city—the mass number—remains unaffected. The identity of the atom changes as it migrates to a new spot on the periodic table. If the atomic number were a street sign, it would be swapped for the previous number, indicating a slight shift in the city's layout.

The atomic number is like an atom's ID, a unique number that reveals how many protons are packed in the nucleus. It determines the element's place on the periodic table and its chemical personality. With each beta decay or electron capture, this number can change, like getting a sticker on your ID every time you learn a new skill. If an atom were a person, the atomic number would be like their name; changing it slightly alters who they are.

The mass number is the total number of protons and neutrons in an atom’s nucleus—think of it as the atom's weight on its driver's license. Unlike the atomic number, the mass number doesn't care about the proton-neutron ratio, just the total count. Whether we’re dealing with beta decay or electron capture, this number typically remains unchanged because we're not adding or removing any protons or neutrons, we're just transforming them. It's like saying whether you're wearing a hat or not doesn't change how much you weigh.