Question

The ‘m’ value for an electron in an atom is equal to the number of m values for l = 1. The electron may be present in
A.$$3d_{x^2-y^2}$$
B.$$5f_{x(x^2-y^2)}$$
C.$$4f_{x^3/z}$$
D.None of the above

Answer 1

Hint: From Schrodinger’s wave equations, we can derive certain quantities that describe the size, shape and orientation in space of the orbitals of the atoms. These quantities are known as quantum numbers.

Complete step by step answer:
The quantities derived from Schrodinger’s wave equations are represented by the letters l, m and n. These letters stand for the quantities mentioned as Orbital angular momentum quantum number, Magnetic quantum number and Principal quantum number respectively.
In the given question, two of these quantities have been discussed, viz. Orbital angular momentum quantum number, i.e. ‘l’ and Magnetic quantum number, i.e. ‘m’.
The relationship between these two quantum numbers can be discussed as follows:

	s orbital	p orbital	d orbital	f orbital
l	0	1	2	3
m	0	-1, 0, 1	-2, -1, 0, 1, 2	-3, -2, -1, 0, 1 ,2, 3

From this table, we can derive the relation between the two quantum numbers. Hence, as per the question, when l =1, the value of m can range from -3,-2,-1, 0, 1,2,3. Hence, the specified electrons belong in the f orbital.

Hence, Option D is the correct option.

Note:
The combination of all quantum numbers of all electrons in an atom is described by a wave function that complies with the Schrödinger equation. Each electron in an atom has a unique set of quantum numbers; according to the Pauli Exclusion Principle, no two electrons can share the same combination of four quantum numbers.