Physics, 29.08.2019 05:40 syyyd423

Using the equation zeff=z−s and assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant, s, calculate zeff for the 2p electrons in both ions

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Answer from: dedrell16

The estimated effective nuclear charge experienced by a 2p electron of chlorine is $\boxed{\text{7}}$ .

Further Explanation:

Effective Nuclear Charge:

It is the charge experienced by the outermost valence electrons of any many-electron atom. This is done by considering the number of shielding electrons that are present around the nucleus.

Slater’s Rule:

It is used to evaluate the effective nuclear charge experienced by an electron in the many-electron atom. According to this rule, the actual nuclear charge experienced by an electron is less than the actual nuclear charge due to screening by the other electrons present in the atom.

The electronic configuration is the distribution of electrons of an atom in the atomic orbitals.

The effective nuclear charge is calculated as follows:

${Z_{{\text{eff}}}} = Z - s$ ......(1)

Here,

Z is the actual nuclear charge.

S is the screening constant.

In KCl compound, two ions are ${{\text{K}}^ + }$ and ${\text{C}}{{\text{l}}^ - }$ .

For ${{\text{K}}^{\text{ + }}}$ ion,

The atomic number of potassium is 19. So its electronic configuration is $\left( {1{s^2}} \right)\left( {2{s^2}2{p^6}} \right)\left( {3{s^2}3{p^6}} \right)\left( {4{s^1}} \right)$ . For 2p orbital, outer shell electrons does not affects the inner shell electrons so the electrons in 3s, 3p, and 4s orbital can be neglected in order to calculate the ${Z_{{\text{eff}}}}$ on a 2p electron. Thus the core electrons in ${{\text{K}}^ + }$ ion are 2 and valance electrons are 8.

Since core electrons contribute 1.00 and valance electrons contribute 0.00 thus the formula to calculate the screening constant for a 2p electron is as follows:

$s = \left[ {\left( {1.00} \right)\left( {{\text{Number of core electrons}}} \right) + \left( {0.00} \right)\left( {{\text{Number of valence electrons}}} \right)} \right]$ ......(2)

Substitute 2 for the number of core electrons and 2 for the number of valence electrons in equation (2).

$\begin{aligned}s&= \left[{\left({1.00}\right)\left( {\text{2}}\right)+\left( {0.00}\right)\left( {\text{8}}\right)} \right]\\&= 2\\\end{aligned}$

Substitute 19 for Z and 2 for s in equation (1) to calculate the effective nuclear charge for a 2p electron in ${{\text{K}}^ + }$ ion.

$\begin{aligned}{Z_{{\text{eff}}}}&=19 - 2\\ &= 17\\\end{aligned}$

So the estimated effective nuclear charge experienced by a 2p electron of ${{\mathbf{K}}^{\mathbf{ + }}}$ ion is 17.

For ${\text{C}}{{\text{l}}^ - }$ ion,

The atomic number of chlorine is 17. So its electronic configuration is $\left( {1{s^2}} \right)\left( {2{s^2}2{p^6}} \right)\left( {3{s^2}3{p^5}} \right)$ . For 2p orbital, outer shell electrons does not affects the inner shell electrons so the electrons in 3s and 3p orbital can be neglected in order to calculate the ${Z_{{\text{eff}}}}$ on a 2p electron. Thus the core electrons in ${\text{C}}{{\text{l}}^ - }$ ion are 2 and valance electrons are 8.

Substitute 2 for the number of core electrons and 2 for the number of valence electrons in equation (2).

$\begin{aligned}s&= \left[{\left({1.00}\right)\left( {\text{2}}\right) + \left( {0.00}\right)\left({\text{8}}\right)} \right]\\&= 2\\\end{aligned}$

Substitute 17 for Z and 2 for s in equation (1) to calculate the effective nuclear charge for a 2p electron.

$\begin{aligned}{Z_{{\text{eff}}}}&= 17 - 2\\&=15\\\end{aligned}$

So the estimated effective nuclear charge experienced by a 2p electron of chlorine is 15.

Learn more:

1. Calculation of the mass of 1 mole of viruses?

2. Determine the moles of water produced:

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Periodic properties of elements

Keywords: Slater’s rule, 2p electron, effective nuclear charge, chlorine, potassium, Cl-, K+, electronic configuration, 17, 19 and atomic number.

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