The atomic number of an element is 15. What is the likely arrangement of the valence and core electrons in a neutral atom of this element?

The element has :

Valence electrons : electrons used in forming bonds (the outer shell)

Core electrons : electrons that belong to atoms except for valence electrons. It is located close to the core and fills the inner shell.  

Electron configurations for an element with the atomic number: 15  1s²2s²2p⁶3s²3p³

Neutral atoms ⇒ atomic number= number of protons=number of electrons

The electron configuration shows that the valence electron of the element = 5(3s²3p³) so the number of Core electrons:  

Core electron = atomic number (total number of electrons) - valence electron  

Core electron = 15 - 15

Core electron = 10