Question

Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value to make the set valid.

What is the correct value for each set?

a) n = 4, ℓ = 2, mℓ = 3, ms = + ½

b) n = 3, ℓ = 3, mℓ = 0, ms = – ½

c) n = 3, ℓ = 2, mℓ = – 1, ms = 0

Answer 1

Let us discuss the accepted values of quantum numbers in the table below-

Name	Symbol	Accepted Values
Principal Quantum no.	n	Positive integers such as 1,2,3... etc.
Secondary or Orbital momentum quantum no.	l	Integers from 0 to (n-1)
Magnetic quantum no.		Integers from -l to +l
Spin quantum no.	s	-(1/2) or +(1/2)

Now, if you observe the above sets of quantum numbers, there is an error in each set like and you can easily figure it out if you follow the table above-

• In first set, value is erroneous, as its value cannot be greater than the 'l' value
• In second set, value of l is incorrect as the value of l should always be less than the principal quantum no n and it can never be equal to n,
• In c, value is '0' which cannot be true. It should be either +(1/2) or -(1/2).

Having familiar with the errors, let us now represent a valid set for all the three cases-

So if you put any of the above row (you have to select any of the values of from the row), you will get the correct set of quantum number. For example, correct set can be

​​​​​​​