The outermost electrons of the element vanadium (atomic #23)
are in which energy level of the atom? how do you know?

The outermost electrons of the element vanadium (A.N.=23) will be in forth energy level (n=4) of the atom.

We know, the capacities of orbital as K,L,M,N = 2,8,8,18 respectively, as 23 is larger than the sum of 2,8,8 it will be in next higher orbital which is forth.

Again, In short, Your Answer would be Forth Energy level

Hope this helps!