How many electrons in an atom can have each of the following quantum number or sublevel designations? (a) 4p (b) n = 3, l = 1, m1 = +1 (c) n = 5, l = 3

a) Six electrons

b) Two electrons

c) Fourteen electrons

Explanation:

n is the principal quantum number and defines the energy level of orbital. The shape of the orbital is described by azimuthal quantum number (l) and it also determine the angular momentum. It values give the following information

l = 0, define s orbital (single orbital)

l = 1, define p orbitals (three orbitals)

l = 2, define d orbitals (five orbitals)

l = 3, define f orbitals (seven orbitals)

These are further specified by magnetic quantum number (ml) which gives the orientation of the orbital. Its value ranges from +1 to -1, for example ml value of five d orbitals are +2, +1, 0, -1, -2. From this information we can predict the number of electrons that will have the given sub-level designations

a) n = 4 and orbital is p, there are three p orbitals as the ml is not defined, so six electrons will have this quantum number

b) In this part, the orbital is defined i.e. ml = +1. A single orbital can have only two electrons, so these electrons will have the given quantum number.

c) l = 3, is for f orbital, which have seven orbitals. The total number of electrons in it is fourteen. All of these electrons will have this quantum number.