Question

What are the total number of orbitals and electrons for m=2 , if there are 30 protons in an atom?
A. 6 orbitals, 12 electrons
B. 5 orbitals, 10 electrons
C. 7 orbitals, 14 electrons
D. 4 orbitals, 8 electrons

Answer 1

Hint: Each electron has magnetic quantum number zero and number of protons is equal to the atomic number. From that, orbitals in it can be determined by electronic configuration, where the number of electrons is just double the number of orbitals.

Complete step-by-step answer:
In an atom, an atomic number is the same as the number of protons present inside the nucleus of that atom. We are given that number of protons are 30 in an atom such that its electronic configuration is \[1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}3{d^{10}}\] because number of electrons are equal to number of protons.
Here, the magnetic quantum number determines the orientation of different orbitals in spatial arrangement. For every corresponding n and l values of an electron, magnetic quantum numbers always have a zero. This means they are spherical shape orbitals. M stands for magnetic quantum number which goes from -1 to+1 , where l is angular quantum number.
We know now that, m value for s(l=0) orbital is only zero, for p(l=1) orbital it can be -1, 0 or +1 and for d orbitals(l=2) it can be -2, -1, 0, +1, +2.
The total number of possible orbitals with the same value of l are 2l +1. So, we can say that there is one s-orbital for l=0, three p-orbitals for l=1 and five d-orbitals for l=2.
As per the electronic configuration, every orbital is fully filled and each has an electron having magnetic quantum number zero. Thus, the total number of orbitals with m=0 are 7. Since every orbital occupies two electrons as per Pauli’s exclusion principle, the number of electrons are 14 in all the 7 orbitals.

Hence, the correct option is (C).

Note: The magnetic quantum number is used to distinguish the orbitals available within a subshell and to calculate the azimuthal component of the orientation of the orbital in space i.e. corresponding l values.