Imagine a universe in which the four quantum numbers can have the same possible values as in our universe except that the angular-momentum quantum number l can have integral values of 0, 1, 2...n + 1 (instead of 0, 1, 2..., n - 1). (a) How many elements would be in the first two rows of the periodic table in this universe?

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Hello everyone today we are being asked the following question. One student made a mistake in determining the quantum numbers of an element. All four were correct. With the exception of the angular momentum quantum number or L. Which had integral values of 012 N instead of 012 and minus one. In these conditions determine the number of electrons that would make up the first two rows of the periodic table. So we'll start with our first row here, row one, We know that our principal quantum number will be in equals one. And by default our angular quantum number will be in -1 including n in minus one Equals and is equal to one. So our first L number zero and then we said in itself which would be one. And of course since we are in the first row we're gonna have a one in front of our orbital and when L equals zero or our angular momentum equals zero, that's gonna give us an s orbital and that can hold a maximum of two elements when L equals one. This is gonna be a p orbital and p orbital's can hold a maximum of six elements And so far we are at eight elements. Now we are going to focus on our 2nd row. So when we have a second row, our principal quantum number is going to be any eagles too. And of course we're going to have N -1. Starting from our end. So we're going to have three angular momentum numbers, we're going to have L equal to one and zero as before we are in the second row. So we will apply the same principle here, we will have a two in front of the orbital for each of these. And so as before, when L equals zero or the angular momentum quantum number zero, we're in the S orbital when Ellie was one, we were in the p orbital and when L equals two, we are in the D orbital. And so as before our S orbital can hold two elements, RP orbital can hold six elements And our d orbital can hold a total of 10 elements. And so we're simply going to add our elements up. So we're going to add the elements And we get elements that comprise the first two rows of the periodic table as our final answer. Overall, I hope this helped. And until next time.

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Key Concepts

Quantum Numbers

Angular Momentum Quantum Number (l)

Periodic Table and Electron Configuration