The equation of Schroedinger for the hydrogen atom in the time-independet, non-relativistic form is a partial differential equation involving the position coordinates (x, y and z). The potential energy term for the proton-electron system is spherically symmetric of the form `-1//4pi in_(0) xx (e^(2)//r)`. THus it is advantages to change over from the cartesian coordinates (x,y and z) to the spherical polar coordinates, (`r, theta` and `phi`). In this form the equation become separable in the radial part involving r and the angular part involving `theta` and `phi`. The probability of locating the electron within a volume element `d tau = 4pi r^(2)dr` is then given `|Psi|^(2)(4pir^(2)dr)`, where `Psi` is a function of r, `theta` and `phi`. With proper conditions imposed on `Psi`, the treatment yields certain functions, `Psi`, known as atomic orbitals which are solutions of the equations. Each function `Psi` correspods to quantum number n, l and m, the principal, the azimuthal and the magnetic quantum number respectively, n has values 1, 2, 3,...., l has values 0, 1, 2, ....(n-1) for each value of n and m (n-1) for each value of n and m `(m_(l))` has values =1, +(l+1),...1,0,-1,-2...-l i.e., (2l+1) values for each value of l. In addition a further quantum number called pin had to be introduced with values `+-1//2`. Any set of four values for n, l , m and s characterizes a spin orbital. Pauli.s exclusion principle states that a given spin orbital can accomodate not more than electron. Further the values l = 0, l=1, l=2, l=3 are designated s,p,d and f orbitals respectively.
How many spin orbitals are there corresponding to n = 3?

Options

A. 9
B. 18
C. 3
D. 6

Answer

B