Question

Which statement is not correct for n=5, m=2?
(A) $l=4$
(B) $l=0,1,2,3$
(C) $l=3$
(D) $l=2,3,4$

Answer 1

Hint: Read about the quantum numbers concept. n is the principal quantum number and m is the magnetic quantum number. l is the azimuthal quantum number. Recollect what each term means and then try to find the wrong option.

Complete step by step answer:
- Quantum numbers are the numbers which identify the state of an electron, specify the energy associated with it and its location around the nucleus.
- Principal quantum number, n represents the main shell in which the electron belongs. It gives the distance of an electron from the nucleus and its energy level. n= 1, 2, 3, 4, 5, 6 and 7.
- Azimuthal quantum number, l represents the subshell or orbital to which the electron belongs. It is also known as secondary, subsidiary, orbital or angular momentum quantum number. It also represents the number of orbitals present in a principal shell. l=0, 1, …, (n-1). For example, for n=1, l=0. For n=2, l=0, 1.
- Magnetic quantum number, m represents to which sub-orbital the electron belongs. It is also known as the orientation quantum number because it gives the distribution of electron clouds in space around the nucleus. It also gives information about how many sub-orbitals correspond to a particular orbital. m= +l to –l

- Now, let’s get back to the question. We have been given n=5 and m=2. So, let’s calculate the values of l.
n=5 so, l=0, 1, 2, 3, 4
- But m should be 2. So, let’s calculate m for each value of l.
l=0, m=0
l=1, m=+1, 0, -1
l=2, m=+2, +1, 0, -1, -2
- Therefore, l value should be 2 or more than 2 to get m value as 2.
- Therefore, we can say that option (B) $l=0,1,2,3$ is incorrect because it has l=0, 1.
So, the correct answer is “Option B”.

Note: Remember, principal quantum number, n= 1, 2, 3, 4, 5, 6 and 7. Azimuthal quantum number or Angular momentum, l=0, 1, …, (n-1). Magnetic quantum number, m= +l to –l. Spin quantum number, s indicates the spin of electron which can be clockwise or anti-clockwise so, $s=+{}^{1}/{}_{2} or -{}^{1}/{}_{2}$ respectively.