Question

find an atom which would have an electron with a quantum number of n=5, l=2, mL=0, mS=1/2 and a valence electron with a quantum number of n=6,l=1, mL=-1, mS=-1/2.

Answer 1

Look at the order of filling for the orbitals. Actually, I think there can be more than one answer when the question says "any" electron with certain quantum numbers. To have n = 6 in the valence shell means the element must follows Ba (56) but can't be as high as Fr(87). Tl (81) appears to be a choice. You can check this out at www.webelements.com.