Question

For the electron of an oxygen atom, which of the following statements is correct?
(A) ${{\text{Z}} _{\text{eff}}} $ for an electron in 2s orbital is the same as${{\text{Z}} _{\text{eff}}} $for an electron in a 1p orbital.
(B) an electron in the 2s orbital has the same energy as an electron in the 2p orbital.
(C) ${{\text{Z}} _{\text{eff}}} $for an electron in 1s orbital is the same as ${{\text{Z}} _{\text{eff}}} $for an electron in a 2s orbital.
(D) the two electrons present in the 2s orbital have spin quantum numbers, $\text{m}{{\text{s}} _{s}} $, but of opposite sign.

Answer 1

Hint: The effective nuclear charge of s-orbitals, nearer to the nucleus, is always higher than the corresponding p, d, f orbitals because of effective nuclear decreases as the distance of the orbital from the nucleus increases and vice-versa. The energy of the orbitals is never the same and each orbital posses’ different energies and each orbital has two electrons in which the orientation of electrons obeys spin quantum number. Now identify the correct statement.

Complete step by step solution:
Oxygen is a non -metal belonging to the p-block category and has the atomic number as 8 and mass number as 16 and its outer shell electronic configuration is $2{{\text{s}} ^ {2}} \text {2} {{\text{p}} ^ {4}} $. To know the correct statements from the above given statements, consider the statements one by one and check it.
(A) The Zeff​ for an electron in a 2s orbital is greater than that in 2p orbital because the electrons of the s-orbitals are nearer to the nucleus and are more tightly held by the nucleus than the electrons of the 2p orbitals and as the distance of the orbital increases from the nucleus, the effective nuclear charge goes on decreasing and vice-versa.
So, the statement (A) is incorrect.
(B) The orbitals cannot have the same energy and each orbital has its own definite energy and the energy of an orbital is governed by the rule n+l. Here, n=principal quantum number and l=azimuthal quantum number. And the lower value of this indicates that the orbital has lower energy and vice-versa.
For 2s-orbital, n+l =2+0 =2
For 2p-orbital, n+l = 2+1=3
So, it is clear that the (n+l) value of 2s-orbital is lower and therefore, its energy is lower than the energy of 2p-orbital.
Hence, the statement (B) is also incorrect.
(C) The Zeff​ for an electron in a 1s orbital is greater than that in 2s orbital because the electrons of the 1s-orbitals are nearer to the nucleus and are more tightly held by the nucleus than the electrons of the 2s orbital and as the distance of the orbital increases from the nucleus, the size of the orbital increases and its effective nuclear charge decreases and vice-versa.
So, the statement (C) is incorrect.
(D) An orbital consists of a maximum of two electrons and their orientation is governed by the spin quantum number which states that the two electrons in the orbital are present together but with the opposite spin i.e. if one electron has +1/2 spin, then the other electron will have -1/2 spin.
So, the statement(D) is correct.

Hence, from the above-given statements option (D) is correct.

Note: The effective nuclear charge and the atomic number are the two different terms. The effective nuclear charge is the charge which an electron carries in the atom due to the effect of nucleus whereas the effective atomic number is defined as the total number of electrons which the central metal atom contains.