Quantum Numbers

Question 1

State the four quantum numbers and their associated letter.

Answer 1

Principal Quantum Number (n)
Orbital Angular Momentum Quantum Number (l)
Magnetic Quantum Number (ml)
Spin Magnetic Quantum Number (ms)

Question 2

Define the Principal Quantum Number (n)

Answer 2

The principal quantum number n indicates the shell or energy level in which the electron is found.

Question 3

Define the range of allowed values for the Principal Quantum Number (n)

Answer 3

The value of n can be set between 1 to n, where n is the value of the outermost shell containing an electron. This quantum number can only be positive, non-zero, and integer values. That is, n=1,2,3,4,..

Question 4

Define the Orbital Angular Momentum Quantum Number (l)

Answer 4

The orbital angular momentum quantum number, l, indicates the subshell of the electron. You can also tell the shape of the atomic orbital with this quantum number.

Question 5

Define the various letters and their associated values of the Orbital Angular Momentum Quantum Number (l)

Answer 5

s subshell corresponds to l=0,
p subshell = 1,
d subshell = 2,
f subshell = 3, and so forth.

Question 6

Define the allowed values for an Orbital Angular Momentum Quantum Number (l), and how it relates to (n).

Answer 6

This quantum number can only be positive and integer values, although it can take on a zero value. In general, for every value of n, there are n values of l. Furthermore, the value of l ranges from 0 to n-1. For example, if n=3, l=0,1,2.

Question 7

Define the Magnetic Quantum Number (ml)

Answer 7

The magnetic quantum number, ml, represents the orbitals of a given subshell.

Question 8

Define the range of allowed values for a Magnetic Quantum Number (ml) given the range l.

Answer 8

For a given l, ml can range from -l to +l. A p subshell (l=1), for instance, can have three orbitals corresponding to ml = -1, 0, +1. In other words, it defines the px, py and pz orbitals of the p subshell. (However, the ml numbers don’t necessarily correspond to a given orbital. The fact that there are three orbitals simply is indicative of the three orbitals of a p subshell.) In general, for a given l, there are 2l+1 possible values for ml; and in a n principal shell, there are n2 orbitals found in that energy level.

Question 9

Definethe Spin Magnetic Quantum Number (ms), and discuss its valid values.

Answer 9

The spin magnetic quantum number can only have a value of either +1/2 or -1/2. The value of 1/2 is the spin quantum number, s, which describes the electron’s spin. Due to the spinning of the electron, it generates a magnetic field. In general, an electron with a ms=+1/2 is called ­­an alpha electron, and one with a ­ms=-1/2 is called a beta electron. No two paired electrons can have the same spin value.