Briefly account for each of the following observations:

(a) Atomic radii decrease in the order Sc > Ti > V.

(b) Densities increase in the order Ti > V > Cr.

Video transcript

All right. Hi, everyone. So for this question, let's provide a brief explanation for each of the following observed rankings. Part one is the ranking based on increasing atomic radii going from molybdenum followed by niobium zirconium and atrium. Next is the ranking based on increasing density which goes from atrium to zirconium, niobium and molybdenum. So now here we have four different answer choices. Each proposing different correlations between the observed rankings and either increasing nuclear charge mass and atomic radius. So the first thing I want to point out here is the location of all four elements listed on the periodic table. Now, it just so happens that all four are deep block elements in the same period. So when I go from left to right in the D block, the first element is atrium followed by zirconium, niobium anne molybdenum. So these are their locations on the periodic table. And the first thing I want to point out here is that this is the same order listed in the text of the question of increasing density. In other words, atrium on the left is the least dense. Whereas molybdenum on the right side, it is the densest whereas the ranking of increasing atomic radii goes in the opposite direction, right? Because according to the text of the question, molybdenum on the right side has the smallest atomic radius and atrium on the left side has the largest atomic radius. So here lets go ahead and discuss why that is the case. And first, I actually want to start off with the trend in the atomic radius. Oops because the first thing that I want to point out here is that as we go along the same period, then the atomic number increases as you go from left to right now, recall that the atomic number corresponds to the number of protons inside of the nucleus. Which means that as the atomic number increases from left to right. So does the number of protons inside the nucleus. So this means that as the number of protons in the nucleus increases as we go from left to right, the charged density of the nucleus itself increases because there are more positive charges inside of the nucleus as the number of protons increases, right. So that comes in handy when we recall the fact that protons are positively charged and therefore attract the negatively charged electrons towards them, right? Because as we increase the positive charge density in the nucleus, then what that means is that electrons are going to be more attracted to the nucleus. And when electrons are more attracted to the nucleus, the admiral itself becomes more compact because now there is less distance between the protons inside of the nucleus and the electrons surrounding it. So the reason why molybdenum on the very right side has the smallest radius of the elements being considered is because it has the greatest atomic number. Therefore, the greatest number of protons inside of the nucleus, which therefore means that electrons are going to be most attracted to the number of protons inside the nucleus of molybdenum, which therefore decreases the distance between them and makes the radius of the atom overall smaller. So the ranking of the atomic radius in the periodic table corresponds to the increasing nuclear charge that can better attract electrons towards the center of the atom. So with that in mind, we can go ahead and discuss the ranking in density that follows the opposite trend as the one or the trend of the atomic radius. Now, what I want to point out here is that the observed ranking in density is the opposite to that of the nucleus or the excuse me, the atomic radius. And the reason for this is because density is equal to the mass divided by the volume. So as we go from left to right across the period, then the mass of the element is increasing. However, the volume, the volume actually decreases because the atomic radius is getting smaller and smaller as we go from left to right. So when we consider the formula for density right density is going to increase as the volume decreases because they are inversely proportional because as the mass increases and volume decreases the ratio between them. Therefore, the density becomes larger and there you have it right. So the reason why we see the trend in the density is because mass increases but the radius and therefore the volume decreases. So with all that being said, if I scroll up here to the choices, the answer is going to be option C. In the multiple choice, the observed ranking in atomic radii is caused by the increasing nuclear charge as you go from left to right of the periodic table. While the observed ranking in density is caused by increasing mass but decreasing radius as you go from left to right of the periodic table. And with that being said, thank you so very much for watching. And I hope you found this helpful.