Question

calculate the effective nuclear charge felt by a 3d electron of chromium atom. (z=24)​

Answer 1

Answer:

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Explanation:

The formula to be used is:

Z* = Z - S

where:

Z* = effective nuclear charge

Z = atomic number of Cr = 24

S = shielding

Let us first calculate S using Slater's rule.

*Write the electronic configuration as follows: (1s)^2 (2s 2p)^8 (3s 3p)^8 (3d)^5 (4s)^1

*Electrons in an "s" or "p" orbit in the same shell as the electron for which you're solving contribute 0.35, electrons in an "s" or "p" orbital in the shell one energy level lower contribute 0.85, and electrons in an "s" or "p" orbital in shells two energy levels and lower contribute 1.

Therefore, the (4s)^1 do not contribute since we are focusing on the 3d orbital. Therefore,

S = (5 x 0.35) + (8 x 0.85) + (10 x 1) = 18.55

Thus,

Z* Z - S = 24 - 18.55 = 5.45

* Electrons in a "d" or "f" orbital in the same shell as the electron for which you're calculating contribute 0.35, and electrons in an "d" or "f" orbital in all lower energy levels contribute 1. Electrons in shells higher than the electron for which you're solving do not contribute to shielding.

Therefore, the (4s)^1 do not contribute since we are focusing on the 3d orbital. Therefore,

S = (4 x 0.35) + (18 x 1) = 19.4

Thus,

Z* = 24 - 19.4 = 4.6

Answer 2

Given that,

The effective nuclear charge felt by a 3d electron of chromium atom.

We know that,

The electronic configuration of chromium

$Cr=1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}3d^{5}$

We need to calculate the effective nuclear charge

Using formula of effective nuclear charge

$Z_{eff}=Z-((valence\ electron -1)\times0.35\times remaining\ electron)$

Put the value into the formula

$Z_{eff}=24-((5-1)\times0.35+18)$

$Z_{eff}=24-19.4$

$Z_{eff}=4.6$

Hence, The effective nuclear charge is 4.6