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?

Question

Accepted Answer

All right. Hi, everyone. So this question says that detailed calculations show that the value of Z effective for the outermost electrons in silicone and chlorine atoms is 4.29 positive and 6.12 positive respectively, or 6.12 positive. What value do you estimate for the effective experienced by the outermost electron in both silicone and chlorine? By assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant. And here we have four different answer choices labeled A through D proposing different values for Z effective. Now recalled c effective represents the effective nuclear charge and it is equal to the atomic number Z subtracted by the shielding constant representing the inner core electrons. That's s so our first task is to find the atomic numbers of both silicone and chlorine according to the periodic table. So for silicone Z is equal to 14, that's its to atomic number. And for Corine that's 17. So now to distinguish between the inner and outer electrons, we have to recall the electronic configurations of both silicone and chlorine. Now this can be achieved by going through the periodic table and adding electrons in the S and P blocks as you go row by row until you reach your desired element. Now, in the case of silicone, the electronic configuration is one S two, two, S two, two P six, three S two and three P two. Now, as for the electronic configuration of chlorine, it's going to be very similar to that of silicone considering they are in the same P block. However, instead of the final orbital here being three P two, in the case of chlorine, it's going to be three P five. So thats one S two, two, S two, two, P six, three S two and finally, three P five. So when it comes to distinguishing between the outer and the inner electrons, we have to distinguish between the energy levels that are present in their electronic configurations. For both silicone and chlorine, we have N equals one, N equals two and N equals three. So in the case of both silicone and chlorine, the electrons that reside in N equals three represent the outer electrons and those in N equals one and N equals two represent the inner electrons. So considering silicone specifically the number of electrons in N equals three totals four, where is the number of electrons? And N equals one and N equals two total 10. So there are four outer electrons and 10 inner electrons. And as for chlorine, the outer electrons are the ones in N equals three. So that's a total of seven and the inner electrons are, those in N equals one nn equals two, which would be 10. So now let's talk about the screening constant recall that the screening constant represents the sum of both the outer and inner electrons multiplied by their respective contributions to the screening constant. Right? According to the question, we're going to assume that valence electrons. In other words, the outer electrons contribute zero to the screening constant. So this means that in calculating the screening constant, we're going to multiply the number of outer electrons by zero, which means that they actually would not contribute anything to the value of the screening concept. For example, in the case of silicone, let me scroll down once more. For the effective nuclear charge of silicone, we're going to take its atomic number 14 and subtract that by the screening constant and the screening constant is equal to the sum of all electrons present multiplied by their contribution to the screening concept. So in the case of the four outer electrons, there will be four multiplied by zero added to 10 inner electrons multiplied by a contribution of one. This expression simplifies to 14, subtracted by 10, which means that Z effective for silicone is equal to four. And so we can do the same thing for chlorine because the Z effective for chlorine is equal to the atomic number 17 subtracted by the screening constant. So in brackets here, that's seven inner electrons, excuse me, outer electrons multiplied by zero, added to 10 inner electrons multiplied by a contribution of one. This expression simplifies to 17, subtracted by 10, which equals that the Z effective of chlorine is seven and there you have it. So here our final answer is going to be option C in the multiple choice because the Z effective of silicone is equal to four and that of chlorine is equal to seven. So with that being said, thank you so very much for watching and I hope you found this helpful.

Verified Solution

Key Concepts

Effective Nuclear Charge (Zeff)

Shielding Effect

Valence and Core Electrons