To determine the atomic number of an element, we can look at the electronic configuration of its cation.
The electronic configuration you provided, 1s^2, 2s^2, 2p^6, indicates that the cation Y^ has a total of 10 electrons.
Since the cation has a positive charge, we can infer that it has lost electrons. Therefore, we subtract the number of lost electrons from the total number of electrons to find the atomic number.
If the cation Y^ has the electronic configuration 1s^2, 2s^2, 2p^6, and a total of 10 electrons, then it has lost 10 - x electrons, where x is the number of lost electrons.
To determine the atomic number, we need to find the element that matches this configuration. The configuration 1s^2, 2s^2, 2p^6 corresponds to the noble gas neon (Ne), which has an atomic number of 10.
Therefore, the element with the cation Y^, having the electronic configuration 1s^2, 2s^2, 2p^6, would have an atomic number of 10.