Question

The electrons identified by the quantum numbers n and l can be placed in the order of increasing energy as:
1. n = 4, l = 1
2. n = 4, l = 0
3. n = 3, l = 2
4. n = 3, l = 1
A) 3 > 4 < 2 < 1
B) 4 < 2 < 3 < 1
C) 2 < 4 < 1 $\leq$ 3
D) 1 < 3 $\leq$ 2 < 4

Answer 1

A set of numbers which is used to describe the position and movement of an electron in an atom is known as quantum number. There are four quantum numbers namely, principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number.

Complete step by step answer:
n and l are the quantum numbers.

Principal quantum number: Principal quantum number is designated by n. The principal quantum number designates the shell of the atom. Principal quantum number ranges from 1, 2, 3, 4….
Azimuthal quantum number: Azimuthal quantum number is designated by l. The azimuthal quantum number designates the subshell of the atom. If l = 0 then it is s-subshell, if l = 1 then it is p-subshell, if l = 2 then it is d-subshell and if l = 3 then it is f-subshell.
We are given four electrons:
1. n = 4, l = 1 : If l = 1 then it is p-subshell. Thus, the electron is in 4p orbital.
2. n = 4, l = 0 : If l = 0 then it is s-subshell. Thus, the electron is in 4s orbital.
3. n = 3, l = 2 : If l = 2 then it is d-subshell. Thus, the electron is in 3d orbital.
4. n = 3, l = 1 : If l = 1 then it is p-subshell. Thus, the electron is in 3p orbital.
The order of increasing energy is as follows:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d and so on.
Thus, for the given electrons, the increasing order of energy is as follows:
3p < 4s < 3d < 4p
Thus, for the given electrons, the increasing order of energy is as follows:
4 < 3 < 2 < 1

Thus, the correct option is (B).

Note: The other two types of quantum numbers are:
Magnetic quantum number: Magnetic quantum number is designated by m. The magnetic quantum number designates the total number of orbitals in the subshell and their orientations. The values of magnetic quantum numbers range between +l to -l.
Spin quantum number: Spin quantum number is designated by s. The spin quantum number designates the spin of the atom. Its values are +1/2 and -1/2.