In this problem, we are going to be considering lithium. We are asked to do several things, the first of which is to write the electron configuration for lithium. That's super simple. It's element number three. So it's one is too to s one as part of a. We are also asked to calculate the effect of nuclear charge and the effective nuclear charge is going to be equal to our nuclear charge minus our core electrons. Which will be 3 -2 equals one. So that's our effective nuclear charge B were given the following information. The energy of an electron in a one electron atom or ion equals -2.18 times 10 To the -18 jewels times Z squared over N squared where Z. Is the nuclear charge. And actually they use the effect of nuclear charge on this one. And this one was answered in your text, I'm going to make a note that they used the effective equals one and N is the principal quantum number, which is to. So in order to calculate what we're asked to do is calculate or estimate the first ionization energy of lithium. In order to do that, we simply took 218 times 10 to the -18 jewels times one squared over two squared. And when I did this I got 545 times 10 to the -19. And that would have been jules per atom. Is the amount of heat required 5.45 Times 10 to the -19 jules per adam to convert that to jules per mole. Was that jules per adam? There's 6.022 Times 10 to the 23rd atoms per mole. And I got for this just cleared my calculator 3.28 Times 10 to the 5th jules per mole. and of course that will equal times 10 to the Second, killer jewels per mole. That is our estimated first ionization energy. You see if I got that right? Yes. Okay, we're going to compare the result with the value on Table 7.4. So that is part C. Compare 328 killer jewels per mole to the value. It said that we got on our next one. Got to see where I wrote that down quickly here. Okay, So on our table. Sorry, it took so long to get that there. We got 520 killer goals per mole and we can see that um that is substantially higher estimate for Z effect. Hang on just a second here. Not going to start this whole thing over, but I'm going to go double check something super fast. Make sure I've got the right values here cheating a little bit but I'm looking in the back of the book. 110. Yes, we're correct. So, um, our estimated value is indeed lower than the text. First ionization energy. Our our estimate for the z effective was a lower limit Pepsi. It didn't account for our core electrons which don't perfectly shield The two S Electron. Okay, there. I feel better about that now. And our last part of this question is D Indy says what value of the effective nuclear charge gives the proper value for ionization energy, Which we said was 520. Killing joules per mole. And we are going to probably use some Slater's rules on here. I think I used a quick Slater's rule on here. Yeah, I did. So I used a quick slater's rule. If we want to get 520 killer joules per mole, and we're going to have that equaling 2.18 times 10 to the -18 jewels over X squared and four. So that was that number squared. We're going to get an ex squared here, or X is going to be About 1.26 as our effective nuclear charge. Now, if I use Slater's rules to figure out what are effectively nuclear charge would be, I'm going to get when I've got one S 2 to S one. I have two electrons That I'm going to multiply by zero, Equals 1.70. So I'm going to take 3 -1.70 Equals 1.30. And compare that to the 1-6. We just calculated that will be very close and notice that that number is a little bit higher because the electrons in my one s don't perfectly shield As indicated by multiple them, multiplying them each by 0.85 instead of multiplying by them by one. And I think that's it.