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Let us write down the electronic configuration (e.c) of the element whose atomic number(Z) =15.

Electronic configuration of Z=15 is,

$1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{3}}$

From this we get to know that there are already 5 electrons in the last/valent shell, hence the number of valence electrons is 5.

Valency is defined as the number or electrons that need to be gained or lost in order to gain maximum stability of the radical. Since there are 5 electrons present, the number of electrons needed to complete the shell to obey octet rule is (8-5) = 3 electrons, hence valency is 3.

There are 18 groups in the periodic table and the 18th group consists of noble gases which have a complete valence shell (also called octet). The element of our discussion needs 3 electrons to gain maximum stability. So, we need to subtract 3 from the 18th group number to find the group number of the element P.

Hence the group number of the element with atomic number(Z)= 15 is 15.