Question

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies.
  1. $n=4,l=2,{{m}_{1}}=-2,{{m}_{s}}=-{1}/{2}\;$
  2. $n=3,l=2,{{m}_{1}}=1,{{m}_{s}}=+{1}/{2}\;$
  3. $n=4,l=1,{{m}_{1}}=0,{{m}_{s}}=+{1}/{2}\;$
  4. $n=3,l=2,{{m}_{1}}=-2,{{m}_{s}}=-{1}/{2}\;$
  5. $n=3,l=1,{{m}_{1}}=-1,{{m}_{s}}=+{1}/{2}\;$
  6. $n=4,l=1,{{m}_{1}}=0,{{m}_{s}}=+{1}/{2}\;$

Answer 1

Hint: We are given the quantum numbers of six electrons and from that we could determine the orbital in which the electron belongs to. We can arrange the electrons in order of increasing energies according to the orbitals which the electron is filled with.

Complete step by step answer:
 -In order to completely describe an electron in an atom, four quantum numbers are needed and they are the Principal Quantum Number(n) , the Azimuthal Quantum Number(l), the Magnetic Quantum Number(${{m}_{l}}$) and the Spin Quantum Number (${{m}_{s}}$).
- The principal quantum number describes the energy level, or electron shell, of an atom, whereas the azimuthal quantum number (also known as angular or orbital quantum number), describes the subshell and also gives the magnitude of the orbital angular momentum.
 - The third or the magnetic quantum number defines the energy levels accessible within a subshell and the Spin quantum number defines the intrinsic angular momentum or spin of the electron within that orbital .
 - If the value of principal quantum number n=4 and azimuthal quantum number $l$=2, then the orbital occupied by the electron is 4d. If n=3 and $l$=2, then the orbital is 3d. If n=4 and $l$=1, then the orbital occupied is 4p.
 - We are given six electrons numbered from 1 to 6 and their corresponding quantum numbers are also given. From the above mentioned criteria of orbitals we can say that the electrons 1, 2,3,4,5 and 6 are present in 4d, 3d, 4p, 3d, 3p and 4p orbitals respectively.
- As we know, s orbital is lower in energy than p and d orbitals. Also if two electrons are occupied in the same orbital such as electron 2 and electron 4 (both in 3d), they will have the same energy. Hence we can arrange the electrons in the increasing order of energies as follows
5(3p) < 2(3d) = 4(3d) < 3(4p) = 6(4p) < 1(4d).
 Or simply we can represent as 5 < 2 = 4 < 3 = 6 < 1

Note: Keep in mind that the orbitals which have the identical energy levels are referred to as degenerate energy levels. Also, according to the Pauli Exclusion Principle, no two electrons can share the same combination of four quantum numbers or in other words each electron in an atom has a unique set of quantum numbers.