Question

Determine the number of electrons of manganese which has zero value of the magnetic quantum number.
(A) 1
(B) 8
(C) 12
(D) 13

Answer 1

The route and mobility of an electron in an atom may be described using quantum numbers. When all of the electrons in an atom's quantum numbers are added together, the Schrodinger equation must be satisfied. Quantum numbers are a collection of numbers that describe the location and energy of an electron in an atom. Principal, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.

Complete answer:
Between spin and azimuthal quantum numbers, the magnetic quantum number comes in third. It divides the sub-shells (such as s,p,d,f) into distinct orbitals, with the electron occupying one of them. It specifies the spatial direction of a certain orbital with a specific energy (n) and form (I).
The number of orbitals in each subshell is 2+1, which is the azimuthal quantum number. We can determine the orbital in each subshell using this method.
Because the magnetic quantum number is determined by the azimuthal quantum number, its value spans from – to +, with 0 being the lowest.
The Schrodinger equation may be used to generate quantum numbers in general and magnetic quantum numbers in particular. To match the equations with the actual world, however, boundaries or constraints must be established. Solving the azimuthal equation of the hydrogen Schrodinger equation yields the magnetic quantum number.
One orbital in each sub energy level has m=0.
Number of electrons of manganese with magnetic quantum number value 0 is 13.
The electronic setup is as follows $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{2}}3{{d}^{5}}$
There is just one electron with m=0 in the 3d subshell. Each subshell has two electrons with m=0 in the remaining subshells.
Hence option D is correct.

Note:
The direction of the angular momentum vector is roughly referred to by the quantum number m. Because all spherical harmonics corresponding to various arbitrary values of m are equal in the absence of a magnetic field, the magnetic quantum number m only influences the electron's energy if it is in one. The magnetic quantum number, as the name implies, defines the energy shift of an atomic orbital owing to an external magnetic field (the Zeeman effect).