Question

An e- has a magnetic quantum number as -3, what is the principal quantum number?
a.) 1
b.) 2
c.) 3
d.) 4

Answer 1

Hint: To answer the principal quantum number of an electron, we should know about different types of quantum numbers. We should know the difference between every quantum number.


Complete step by step solution:
Let us know about quantum numbers. We need to completely describe an electron in an atom, four quantum numbers are needed: energy (n), angular momentum (ℓ), magnetic moment (mℓ), and spin ($${\text{m}}_{\text{s}}$$). We should know that the first quantum number describes the electron shell, or energy level, of an atom. We should know that the value of n, range from 1 to the shell containing the outermost electron of that atom. Now, we will describe the azimuthal quantum number. We should know that second quantum number, known as the angular or orbital quantum number. We should know that ℓ = 0 is called an s orbital, ℓ = 1 a p orbital, ℓ = 2 a d orbital, and ℓ = 3 an f orbital. The value of ℓ ranges from 0 to n − 1 because the first p orbital (ℓ = 1) appears in the second electron shell.
We should know that the principal quantum number (n) has its value 1, 2, 3....
So, now we can say that Azimuthal quantum number (l) has values ranging from 0 to (n-1).
And in the last we can say that, magnetic quantum number (m) value ranges from negative l to positive l.
Now, let us calculate the above question. As given in the question, the electron has magnetic quantum number -3. So, the question is asking us to calculate the principal quantum number.
Magnetic quantum number (m) of electron = -3
So, as per the above statement magnetic quantum number has value negative l to positive l.
For a given value of l, m can have values −3, −2, −1, 0, +1, +2, and +3.
For a given value of n, l can have values 0, 1, 2 ... (n−1)
Now, we can say that its principal quantum number is 4.
From the above discussion we can say that option D is correct.


Note: There is another quantum number, which we know by name spin quantum number. We should know that it determines the spin of an electron. We should know that it describes the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum.