The electrons in an atoms orbit around the nucleus. These orbits are arranges in several layers called shells there are theoretically 7 such shells are possible. Starting from the shells closest to the nucleus these are designates as shells K, L, M, N, O, P and Q. The maximum numbers of electrons that each shell can contain is fixed. Further electrons in any shell up to shell O exist only when the maximum possible numbers of electron in all previous shell are present.
In the given question the number of electrons in shell M is given as 5, against the maximum 8 possible electrons n that shell. This means that there are no electrons beyond shell M and the number of electrons in shell K and L is equal to minimum number of electrons in these shells, which is 2 and 8 respectively. Thus actual number of electrons in the given element is equal to 15.
The element corresponding to 15 electrons is phosphorus with chemical symbol P. It belongs to the "other non metals" group of periodic table.
In order to identify the element, first we have to find it's atomic number, Z (the number of protons). Also we know that the number of protons is equal to the number of electrons.
We don't know the number of protons but we can find out the number of electrons, knowing that the number of electrons of the M level is 5. This means that the levels K and L have been occupied with 10 electrons, 2 on the K level and 8 on the L level. The total number of electrons of the element is 2+8+5=15 electrons. That means that we have also 15 protons and, in this way, we've found out the atomic number Z=15. Searching on periodic table, we'll find on the 15th position the element phosphorus, P.
Phosphorus, P is located on the 5th group (column) and the 3rd period (row) of the periodic table.
To find out the number of neutrons, we know that atomic mass, A=31, is equal with the sum of the number of protons, Z, and the number of neutrons, n:
So, the number of neutrons is: