For the electrons of oxygen atom, which of the following statements is correct?

Concept :

• Z_eff value or the effective nuclear charge on any electron depends on the distance between the electron and the nucleus
• Energy of an electron in an orbital can be calculated by the Aufbau principle. For an electron the energy is (n+l) where n is principle quantum number and l is azimuthal quantum number
• According to the Pauli’s exclusion principle no two electron in an atom should have same set of four quantum number

Explanation :

Option 1

• In oxygen atom the RDF of 2s and 2p is as below

• From graph it is clear that 2s orbital is more penetrated to the nucleus than 2p orbital
• So the electrons in 2s orbital is more tightly bound than that of electrons in 2p orbital
• Thus the Zeff or effective nuclear charge on electrons of 2s orbital greater than that of electrons in 2p orbital

Option 2

• The energy of an orbital is given by (n+l)
• For 2s orbital, n=2 and l=0 so (n+l) = 2
• For 2p orbital, n=2 and l=1 so (n+l) = 3
• So the energy of 2p orbital is greater than 2s orbital

Option 3

The RDF plot of 1s and 2s orbital is

• From the plot it is clear that 1s is more closer to the nucleus than 2s
• Even 1s is the nearest orbital of nucleus
• So electron in 1s orbital is tightly bound than electrons in 2s orbital
• As a result the Zeff is greater on the electrons of 1s than that of 2s

Option 4

• For 2s orbital , principal quantum number (n) = 2 , azimuthal quantum number (l) = 0

Magnetic quantum number (m_l) = 0

• According to the Pauli’s exclusion principle no two electron in an atom should have same set of four quantum number , so spin quantum number (m_s) has to be different for two electrons
• spin quantum number may be + ½ or – ½
• so if one electron has m_s =+ ½ then others has must m_s = - ½

conclusion :

Option 1 is wrong as it says Zeff of an electron in 2s orbital is same Zeff in 2p orbital but the Zeff of an electron in 2s orbital is greater than 2p orbital

Option 2 is wrong as it says an electron in 2s orbital has same energy as an electron in 2p orbital but the energy of an electron in 2s orbital is greater than an electron in 2p orbital

Option 3 is wrong as it says Zeff of  an electron in 1s is same as an electron in 2s orbital but Zeff of an electron in 1s orbital is greater than Zeff of an electron in 2s orbital

Option 4 is right because the spin quantum number of two electron in 2s orbital is + ½ and - ½ i.e. that are same in value but has negative sign

So the correct option is (4)