Why can Copper have both a +1 and +2 oxidation state?

Yeah, I know that, but why can Copper lose either one or two while cadmium only has a +2 OS. I think the answer has something to do with valence electrons, but I'm not sure exactly.

Copper can have both a +1 and +2 oxidation state due to its unique electron configuration and the availability of its d-orbitals. To understand why copper exhibits these different oxidation states, we need to consider the electronic structure of copper atoms and the rules governing oxidation states.

Copper belongs to Group 11 of the periodic table and has an atomic number of 29. In its ground state, a copper atom has the electron configuration [Ar] 3d^10 4s^1. The valence shell of an atom primarily consists of the outermost s and p orbitals. However, in the case of copper, the 3d orbitals are relatively close in energy to the 4s orbital, making it possible for copper to accommodate different oxidation states.

In its +1 oxidation state, a copper atom loses its single 4s electron, resulting in a configuration of [Ar] 3d^10. This configuration is particularly stable since it corresponds to a completely filled d-orbital, known as a "pseudo-noble gas" configuration.

In its +2 oxidation state, a copper atom loses both its 4s and one of its 3d electrons. This leads to a configuration of [Ar] 3d^9. Though not as stable as the completely filled 3d^10 configuration, it is still energetically favorable due to the presence of paired electrons in the d-orbital, which exhibit some degree of electron-electron repulsion.

The ability of copper to adopt both the +1 and +2 oxidation states makes it versatile in forming a variety of compounds, including copper(I) and copper(II) compounds, with different chemical and physical properties.

To determine the oxidation states of elements, it is often helpful to consider the element's electron configuration, periodic trends, and the compounds it forms. Additionally, referencing a reliable source, such as textbooks or scientific articles, can provide further details on specific elements' oxidation states in various compounds.

Because it can lose either 1 or 2 electrons.

I think the comparison you are making is not a valid one for Cd has an electron configuration of [Kr]4d10 5s2. It is easy enough to see that Cd loses the two outside (valence) electrons and does not have a great tendency to delve into the lower 4d10 shell (which we usually think of as closed). Cd is quite similar to Zn ion in this respect. Thus the common oxidation state for both Zn and Cd is +2.

I think the pertinent question you may be asking is why does Cu lose two electrons at all? And why aren't most copper compounds Cu+1 and not Cu+2 since the electron configuration is
1s2 2s2 2p6 3s2 3p6 3d10 4s1 = 29.
It is easy enough to understand why copper loses a single electron to form +1 copper compounds. Why it loses two is much much more complex. It turns out that there are MANY more compounds of Cu+2 than of Cu+1 which makes it even more confusing. The answer lies mostly in the environment in which copper finds itself. The solvation energy of the +2 ion (for solutions), the lattice energy of solid Cu+2 vs Cu+1 compounds, and the ability to form complex ions with the d,s, and p orbitals (with variable stabilities), all favor the +2 ion. That isn't a definitive answer, I know, but it may give you some insight into what is going on. The best answer I can give, which, again, is not definitive, is that "that is the nature of the beast." The main reason this can happen is because the relative energy levels of the 3d and 4s orbitals when they are almost or completely filled is so close to each other that the deciding factor is what complex or what compound is being formed. I hope this helps.