Detailed calculations show that the value of Zeff for the outermo...

Question

Detailed calculations show that the value of Zeff for the outermost 
electrons in Si and Cl atoms is 4.29+ and 6.12+, respectively. 
(a) What value do you estimate for Zeff experienced by 
the outermost electron in both Si and Cl by assuming core 
electrons contribute 1.00 and valence electrons contribute 
0.00 to the screening constant?

Accepted Answer

welcome back everyone in this example, we're assuming our core electrons give one and valence electrons give zero to our screening constant. We need to calculate the effective nuclear charge of the outermost electrons of germanium and to lorient. So what they mean by outermost electrons we should recall is our valence electrons. And we need to begin by drawing out the electron configuration of Germanium and then Tillery. Um so beginning with Germanium on our periodic tables, we see that it has a atomic number equal to a value of 32. So according to its configuration on the periodic table, we would begin with one S. Two. Moving on up in energy, we go up to two S two and then two P six. Moving on up an energy we get to the three S to sub level and then the three P six sub level where then we get to our D block on a periodic table which we should recall begins at the fourth energy level and we need to fully fill in our D block here. So we would have three D 10. And as we stated, it's at the fourth energy level, meaning we go through the four S to sub level and then we get to the four p block where we only count for a total of two units to land owner adam germanium. So what we should recognize is that because this is the outermost energy level. These represent our This is our valence shell and these exponents here are four valence electrons. And what that means for everything else in our configuration is that all the exponents here represent our core electrons. So we have a total of when we add this together, 28 core electrons and everything added together. Core and valence electrons would give us our atomic number 32 as we have for Germanium on the periodic table. And so what we need to do is figure out how much is contributing to our shielding or screening constant according to the prompt. And so we would say that the total screening and this is of the nucleus of our germanium atom. So the total screening caused by our valence first let's calculate would be our four that we counted according to our configuration multiplied by the value zero given in the prompt. And that gives us a total screening of our valence electrons equal to zero. So then moving on to the total screening By our core electrons we counted above that. We have a total of 28 core electrons which we will multiply by the screening constant given in the prompt as 1.00 for our core electrons. And that gives us just 28. And so what this means is that our total shielding or screening Is equal to a value of 0-plus 28. Which just gives us 28. Now recall that our shielding or screening constant is represented as a capital S. And so we can say that to calculate the effective nuclear charge of germanium, We're going to take our atomic number of Germanium which is the value Z. And we're going to subtract it from our screening constant. And this is going to give us our effective nuclear charge of Germanium. And so let's plug in those values that we know below. So we know our atomic number of Germanium is 32 as we stated above. And we know that our screening constant as we calculated above is the value of our core and valence electrons. And this gives us a different equal to a value of four. And so this would be actually our first answer here for our effective nuclear charge of germanium. And now we can follow the same steps to get the same value or a different value but the same idea for our second atom which is to Laurie. Um So going down for more room, we have to lori. Um And according to our periodic table and according to the problems we have a neutral atom. So we should recall that to Lori. Um atomic number is the value being 52. And so going to its electron configuration, we would begin at the one S to sublevel. Moving up in energy, we go through the two S. Two and then two P six sublevel moving up higher in energy we get to the three S to sub level as well as filling out the three P six sub level. Then when we get to the fourth energy level, we fill in our D block. So we have three D 10 where we go through our four s to sub level and the four p six sublevel moving up in our configuration. We get to the fifth energy level where we have our fourth energy level of our D block. So we have four D 10. We also should recognize that we go through our F block. So we would have four F. And actually we don't need to include that because we actually don't go through our F block because recall that the F block begins at atomic number 57 as we stated to Laurie um is only atomic number 52. So we can exclude that from our configuration and we would end off with the 40 10 um configuration where our highest energy level would be the five S two and then five p four sub level where we have just five P four because that is what it takes to land on our atom for to Laurie. Um and so we should recognize that our valence shell is the outermost energy level which is our fifth energy level here and consist of a total of we would say six valence electrons. Whereas as far as our core electrons, we would have all of these exponents here representing our core electrons And adding the sum here, we would say we have a total of 46 core electrons and then adding these two values up would give us our atomic number being 52. And so as we did above we're going to get our total screening from our valence first And that would be our six valence electrons multiplied by the screening given in the prompt being a value of 0.00 which gives us just zero. And then we would say total screening of our core electrons. According to our calculation for the configuration we have 46 core electrons multiplied by their screening given from the prompt being one. And this gives us our value 46. So we would say that our total shielding constant is equal to a value of zero plus 46 which just gives us a value of 46. And so this allows us to calculate our effective nuclear charge of two Laurie. Um and we would say that that's equal to the atomic number minus our total screening constant. Which is going to be a value of the atomic number as we stated above is minus our total screening being 46. And this gives us our effective nuclear charge of two Laurie um equal to a value of six. And so this would be our second and final answer to complete this example. So everything highlighted in yellow represents are too effective effective nuclear charges of first germanium and then to Laurie. Um so I hope everything I went through is clear this corresponds to the multiple choice answer being see as the correct choice. So if you have any questions, just leave them down below and I'll see everyone in the next practice video.

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