(a) The total number of electron shells in an atom determines the period to which the element belongs, and the valence electrons determine the group to which it will belong. So with the help of electronic configuration we can figure out the period and group number of an element.

Elements with one and two valence electrons belong to group 1 and 2 respectively, while to determine the group number of elements with 3 to 8 valence electrons, we add 10 to their valence electrons.

For example an element X has atomic number 15

Its configuration will be:

K shell has 2 electrons, L will have 8, and the remaining 5 will be placed in M shell

Since it has three shells it belongs to period 3 and with 5 valence electrons the element will be placed in five plus ten that is the 15th group

So with the help of electronic configuration we can figure out the period and group number of an element.

(b) Atomic number = Number of protons

Hence, number of protons in K atom = 19

Number of neutrons = Mass number − Atomic number

Hence, number of neutrons in K atom = 39−19 = 20

Number of electrons = Number of protons

Hence, number of electrons = 19

And electronic configuration of K atom = 2, 8, 8, 1

Since K atom has 4 shells, hence it belongs to fourth period.

With one valence electron, it belongs to group 1

Number of protons in P atom = 15

Number of neutrons in P atom = 31−15 = 16

Number of electrons in P atom = 15

And electronic configuration of P atom = 2, 8, 5

Since it has three shells, it belongs to period 3 and with 5 valence electrons Phosphorus is found in five plus ten that is 15th group.