Question

Valence electron of zinc atom possesses the quantum numbers n= 3, l = 2, m = +2 to -2 and s= + $ \dfrac{1}{2} $ or - $ \dfrac{1}{2} $ .

A. True

B. False

Answer 1

Hint: We should know that the value of n ranges from 1 to the shell containing the outermost electron of that atom. The Azimuthal Quantum Number is ℓ, and 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. The values of m range from − ℓ to ℓ, with integer steps between them. The values of s range from −s to s. An electron has spin  $ s = \dfrac{1}{2} $ .

Complete step-by-step answer:

We use four quantum numbers to completely describe an electron in an atom, four quantum numbers are: energy (n), angular momentum (ℓ), magnetic moment (m), and spin (s). Now, one by one we will know about each quantum number:

The Principal Quantum Number: The first quantum number describes the electron shell, or energy level, of an atom. Value of n ranges from 1 to a shell containing the outermost electron of that atom. For example, in Zinc (Zn), the electronic configuration is [Ar]  $ 3{{d}^{10}}4{{s}^{2}} $ . The outermost valence electron is in the shell with energy level 3, so an electron in Zinc can have an n value from 1 to 3. So, n=3, in Zinc.

The Azimuthal Quantum Number: We should note that in chemistry, 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 (n = 2), the first d orbital (ℓ = 2) appears in the third shell (n = 3), and so on. So, if we take zinc then n=3 in zinc, it will be equal to 2. So, ℓ=2 for zinc.

The Magnetic Quantum Number: We should note that the values of m range from − ℓ to ℓ, with integer steps between them. So, we know that in zinc, ℓ=2. So, the value of m will be from +2 to -2.

The Spin Projection Quantum Number: the values of s range from −s to s, where s is the spin quantum number. And we know that an electron has spin s =  $ \dfrac{1}{2} $  consequently s will be ±  $ \dfrac{1}{2} $ .

From the above discussion, now we know that the statement that is provided in the question is true.

Zinc atoms possess the quantum numbers n= 3, l = 2, m = +2 to -2 and s= +1/2 or -1/2 is true.

Note:
For solving of these types of questions we should carefully read this table:

Name	Symbol	Orbital meaning	Range of values	Value examples
Principal quantum number	n	shell	1 ≤ n	n = 1, 2, 3, …
Azimuthal quantum number (angular momentum)	ℓ	Subshell (s orbital is listed as 0, p orbital as 1 etc.)	0 ≤ ℓ ≤ n − 1	for n = 3: ℓ = 0, 1, 2 (s, p, d)
Magnetic quantum number (projection of angular momentum)	mℓ	energy shift (orientation of the subshell's shape)	−ℓ ≤ mℓ ≤ ℓ	for ℓ = 2: ℓ= −2, −1, 0, 1, 2
Spin quantum number	ms	spin of the electron (−\[\dfrac{1}{2}~\]= "spin down", \[\dfrac{1}{2}~\]= "spin up")	−s ≤ ms ≤ s	for an electron s = \[\dfrac{1}{2}~\], so s = −\[\dfrac{1}{2}~\], +\[\dfrac{1}{2}~\].