Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. the four quantum numbers, the principal quantum number ( n ) , the angular momentum quantum number ( ) , the magnetic quantum number ( m ) , and the spin quantum number ( m s ) have strict rules which govern the possible values.

Angular momentum quantum number is also known as Azimuthal or subsidiary quantum number (l)

Explanation:

There are 4 types of Quantum numbers namely:

Principal quantum number: This quantum number describe the shell or orbits electrons can be found. it is denoted as 'n'. It can take values from n= 1, 2, 3, 4which represent K, L, M, N shells. Angular momentum quantum number: This is also referred to as Azimuthal or subsidiary quantum number. It describes the sub-orbits or orbitals that electrons can be found. It is dependent on principal quantum number. it denoted as 'l". l can take the value from 0 to n-1. when l=0 (s-orbital), l=1 ( p orbital), l =2 (d-orbital) and l =3 (f-orbital). Magnetic quantum number: This quantum number describe the degenerate orbitals or sub-orbitals electrons are found. It is denoted as 'm'. m values ranges from -l 0+l. Magnetic quantum number depends on  Azimuthal quantum number. Spin quantum number: It describes the orientation of electrons. It is denoted as 's'. It assumes the value of +1/2 and -1/2.

    5.5 n======    assuming that      we have      m = 0.145 kg    a = 38 m/s²therefore    5.51 n, but two significant figures.final answer: 5.5 n