Chapter 5, Problem 89APP

Interpretation Introduction

Interpretation: The possible orbitals in an atom should be determined.

Concept Introduction: The distribution of electrons in an atom is described by the use of quantum numbers used by the Bohr model one-dimensional model. The most important information that is the size of the atom is determined by the principal quantum number denoted by symbol n . Other quantum numbers are angular and magnetic quantum numbers which describes shape and orientation in the space of the orbitals of the atom.

The forth quantum number is spin quantum number which is denoted by symbol s and determined the spin of the electron if it is clockwise or anticlockwise.

The all four quantum numbers are explained in detail as follows:

Principal quantum number (n) determines the size of the orbital. The orbital with principal quantum number 2 is larger than the value 1. This also determines the energy of the orbital, as the value of n increases the energy of the orbital increases as its distance from the nucleus increases.

Angular quantum number (l) determined the shape of the orbital. For $l=0$ , the shape of the orbital is sphere, for $l=1$ , the shape of orbital is polar and that for $l=2$ is cloverleaf.

The rules for the allowed quantum numbers combinations are as follows:

1. All the three quantum numbers ( n, l and m ) describes the orbital of an atom and they are integers.
2. The principal quantum number, n value cannot be zero. Thus, the values allowed for the principal quantum number are 1, 2, 3, 4, and so on.
3. The value of angular quantum number, l can be between 0 to n-1. Thus, if value of n is equal to 3 the value of l can be 0, 1 or 2.
4. The value of magnetic quantum number, m can be between − l to +l . Thus, if value of l is equal to 2, m can be wither -2, -1, 0, +1, or +2

For same number of principal quantum number, an orbital form a shell. The first character denotes the shell and the second identifies the sub-shell.

Here, for s orbital value of $l=0$ , for p orbital it is $l=1$ , for d orbital it is $l=2$ and for f it is 3.