What element has 17 electrons and 8 valence electrons?

Answer 1

It is impossible.

If an element has 17 electrons, you have

2 electrons on the shell K
8 electrons on the shell L
7 electrons on the shell m which is the valence shell

There is no alternative. The element is chlorine

Answer 2

If the element is neutral, than it has atomic number 17. This is one atom left from the noble case argon (18 - Ar) and that is chlorum (17 - Cl).
In its ground state, the electronic configuration of Cl is:

1s2 2s2 2p6 3s2 3p5

so, it has 7 valence electrons. However, if one of the inner atoms is excited, the atom could have 8 valence electrons. But, this is usually an unstable state, which will last for a short time before one of the electrons falls in the empty inner state, resulting in an emission of a Kbeta od Lalpha X - ray photon. Though, due to some selection rules, some of the transitions may be forbidden.