Since the element is in 17th group it will have 7 valence electrons and since it has 3 shells (and the valence shell has 7 electrons in it) it will have the other two shells filled completely. Hence, according to the octet rule the electronic configuration would be 2,8,7. This implies that the atomic number of this element would be 2+8+7 = 17.( Hence, the element is chlorine.) The subshell configuration (based on Aufbau's Principle) 1s^{1 }2s^{2 }2p^{6 }3s^{2 }3p^{5}

Since it has 3 shells it will be in the 3rd Period.