Question

Using the s, p, d notation designate the orbitals with the following quantum numbers.
A. n=4; l=2
B. n=3; l=2
C. n=2; l=0
D. n=3; l=1

Answer 1

The atomic model which is based on the particle and wave nature of the electron is known as the wave or quantum mechanical model of the atom. For an atom there are a number of solutions to the wave equation which are acceptable and each orbital may be described uniquely by a set of three quantum numbers n, l and m.

Complete answer:
Let us discuss the numbers in terms of which quantum mechanics predicts the results,
Principal quantum number: it is denoted by the letter ‘n’ and gives the information about the principal energy level or shell to which the electron belongs. It can have any positive integral values except zero. It gives information about
The number of subshells present in the main shell.
‘l’ can have any integral value ranging from 0 to n-1.
For 1st shell, n=1( l can have only one value that is l=0)
For the second shell, n=2 ( l can have two values that is l=0,1) and so on..
Subsidiary quantum number or azimuthal number (l): it gives the information about the shapes of the various subshells present within the same principal shell and relative order of energies of various orbitals within the same shell.
Now let us understand the s , p and d orbitals to solve the above question. Therefore for
s-orbitals:( l=0) these orbitals are spherical and symmetrical about the nucleus.
p-orbitals: (l=1) these have a directional character and are dumb bell in shape.
d-orbital: (l=2) they have a double dumbbell shape shell.
Therefore for n=4,l=2 makes 4d orbital because l=2 gives the value for d-orbital, for n=3, l=2 the resulting orbital is 3d, for n=2, l=0 the resulting orbital is 2s and for n=3, l=1 the resulting orbital is 3p orbital.

Note:
s, p and d tell the shape and size of the orbitals which is determined by ‘l’ and the size of the orbital increases with the increase in value of the principal quantum number (n).