#### Answer

There are 10 core electrons, 7 valence electrons and 1 unpaired electron in chlorine.

#### Work Step by Step

Chlorine has 17 electrons. The electron configuration of chlorine is $$Cl: 1s^22s^22p^63s^23p^5$$
The nearest noble gas element of lower atomic number is $Ne$, which has the electron configuration $1s^22s^22p^6$. Therefore, the condensed electron configuration of chlorine is $$Cl: [Ne]3s^23p^5$$
1) Looking here, we see that there are 10 inner-shell electrons (those that occupy the first and second shells) and 7 outer-shell electrons (those that occupy the third shell). Also, since chlorine has the atomic number less than 30, all outer-shell electrons are valence electrons.
Therefore, there are 10 core electrons and 7 valence electrons.
2) The unpaired electrons are those who does not have the accompanying electrons which have the opposite electron spin in an orbital.
We see from the electron configuration of chlorine that the first and second shells and the s-subshell of the third shell have been fully occupied.
Therefore, let's look at the p subshell of the third shell.
The maximum number of electrons that a p subshell can have is 6 (p subshell has 3 orbitals, each orbital can carry 2 electrons at most). Here, only 5 electrons are present. According to Hund's rule, since p subshell has only 3 orbitals, and each orbital can carry at most 2 electrons, 2 orbitals would each carry 2 electrons, leaving 1 orbital having only 1 electron.
Therefore, there are 1 unpaired electron in chlorine.