An ion ##”M”^(3+)## has 10 electrons and 14 neutrons what is the atomic number and mass number of M?

##Z = 13##
##A = 27##
Start by making sure that you know what you’re looking for here.
An element’s , ##Z##, tells you how many protons that element contains in its nucleus.
Every element in has an unique . If two atoms have the same atomic number, then they are of the same element.
An atom’s , ##A##, tells you how many protons and neutrons can be found in that atom’s nucleus.
##color(blue)(A = Z + “no. of neutrons”)##
Another important thing to remember is that neutral atoms have equal numbers of protons in the nucleus and electrons surrounding the nucleus.
Notice that the problem provides you with an ion of element ##”M”##. Ions are formed when an element either loses electrons, in which case you get a positively charged ion, or cation, or gains electrons, in which case you get a negatively charged ion, or anion.
In your case, the ion is said to have a ##3+## charge. This means that the neutral atom of element ##”M”## lost three electrons in order to form the ##”M”^(3+)## cation.
Since the cation is said to contain ##10## electrons, you can say that the neutral atom contained
##”10 e”^(-) + “3 e”^(-) = “13 e”^(-)##
Since a neutral atom has equal number of electrons and protons, you can say that the nucleus of ##”M”## contains ##13## protons.
Therefore, the atomic number of ##”M”## is equal to
##Z = 13 ->## aluminium
The of the atom will be
##A = Z + 14 = 13 + 14 = color(green)(27)##
You can thus say that you are dealing with the aluminium-27 isotope of aluminium.