Question

Calculate the effective nuclear charge of the last electron in an atom whose configuration is\[1{s^2}2{s^2}2{p^6}3{s^2}3{p^5}\].

Answer 1

Hint: We have to determine the effective nuclear charge of an atom. Determining effective nuclear charge entails the understanding of the Z and \[\sigma \] values. Z is the atomic number, and σ value requires the use of Slater’s Rules to determine an electron shielding value between the nucleus and the electron.

Complete step by step solution:
We use the following formula to determine the effective nuclear charge.
\[{Z_{eff}} = {\text{ }}Z{\text{ }}-\sigma \]
Where,
\[{Z_{eff}}\] is the effective nuclear charge or Z effective
Z is the number of protons in the nucleus, the atomic number
\[\sigma \]is the average amount of electron density between the nucleus and the electron
Complete step by step answer:
The electronic configuration of an atom given is: \[1{s^2}2{s^2}2{p^6}3{s^2}3{p^5}\].
So here, we can see atomic number of element = Z = 17
Shielding can be calculated as follows:
shielding = \[\sigma \] = [(0.35 × No. of other electrons in nth shell)] + (0.85 × No. of electrons in (n - 1)th shell) + (1.00 × total number of electrons in the inner shells)
We can use the equation to find the shielding energy.
Shielding = \[\sigma \] =\[\;\left[ {\left( {0.35 \times 6} \right) + \left( {0.85 \times 8} \right) + \left( {1 \times 2} \right)} \right]\]
shielding = \[\sigma \] = \[10.9\]
Substituting the values in the formula, we get
\[{Z_{eff}} = {\text{ }}Z{\text{ }}-\sigma \]
\[Zeff{\text{ }} = {\text{ }}Effective{\text{ }}nuclear{\text{ }}charge{\text{ }} = {\text{ }}17{\text{ }}-{\text{ }}10.9\]
Therefore, \[Zeff{\text{ }} = {\text{ }}6.1\]
Hence, the effective nuclear charge of the last electron in an atom whose configuration is \[1{s^2}2{s^2}2{p^6}3{s^2}3{p^5}\] , is \[Zeff{\text{ }} = {\text{ }}6.1\]

Note: We must remember that the number of electrons in the atom is equal to the atomic number of the element. We should know about determining the atomic number using the electronic configuration given. Read more about Slater’s rule in determining the effective nuclear charge.
We must understand Slater's rules to provide numerical values for the effective nuclear charge in an atom. Each electron has experienced less than the actual nuclear charge, because of shielding or screening by the other electrons.