Final answer:
There are 6 known elements with atoms, in their ground state, that have valence electrons with quantum numbers n=5 and l=1.
Step-by-step explanation:
In order to determine the number of known elements that have atoms, in their ground state, with valence electrons whose quantum numbers are n=5 and l=1, we need to consider the electronic configuration of these elements. The quantum numbers n and l represent the principal quantum number and the azimuthal quantum number, respectively.
For n=5 and l=1, the possible values of m are -1, 0, and 1. Each of these values represents a separate subshell. Within each subshell, there can be a maximum of 2 electrons. So, in total, there are 6 possible valence electrons with these quantum numbers.