Ionic Radius and Isoelectronic Species

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take two ions, nitrogen three minus and aluminium three plus. Count their electrons, and both have exactly ten. Same number of electrons, so they should be about the same size, right? But the nitrogen ion has a radius of one hundred and seventy one picometres, and the aluminium ion just fifty four. That is more than three times bigger, with the same ten electrons! So what is going on here? Let's find out what really decides the size of an ion. Questions on this come up often in JEE, so let's begin.

0:40Cations shrink, anions grow

Alright, let's start with a simple question. When an atom loses electrons, it becomes a positive ion, called a cation. So tell me, does it grow or does it shrink? It shrinks, yes, exactly! The nucleus is the same, but now it holds fewer electrons. The double arrow on screen means implies, so a cation is smaller than its parent atom. Okay? Look at sodium. The sodium atom has a radius of one hundred and eighty six picometres; the p m on screen means picometres. The arrow takes us to the sodium ion, with a small raised plus sign for its one positive charge, and its radius, in brackets, is only one hundred and two picometres. Why such a big drop? Sodium loses its only outer electron, so a whole shell, the third shell, disappears. Clear? Now the opposite case. When an atom gains electrons, it becomes a negative ion, called an anion. Same nucleus, but more electrons, so there is more repulsion between the electrons. So an anion is larger than its parent atom. Got it?

1:49One element, different charges

Now let's push this further. Iron can lose two electrons to become iron two plus, or three electrons to become iron three plus. So which of these three is the smallest? Iron three plus, that is correct! Read the line with me, where each greater than sign means a larger radius. Iron is larger than iron two plus, which is larger than iron three plus. Right? The nucleus stays the same, and every electron removed makes the ion smaller. So for one element, the higher the positive charge, the smaller the ion. With me?

2:24Isoelectronic species

Now the most important idea of today. Isoelectronic species are atoms or ions with the same number of electrons. Iso means same, so isoelectronic means same electrons. Okay? Here is the famous ten electron family. Nitrogen three minus, oxygen two minus, fluorine minus, sodium plus, magnesium two plus, and aluminium three plus. The small raised numbers and signs are their charges. Check one with me: nitrogen has seven electrons and gains three, which gives ten. Aluminium has thirteen and loses three, which also gives ten. All ten, right? Now their nuclear charge, capital Z, the number of protons: seven, eight, nine, eleven, twelve and thirteen. The same ten electrons in every ion, but the pull keeps rising. So which ion is the smallest? Aluminium three plus, yes, exactly! Thirteen protons pull on just ten electrons. So the rule is: among isoelectronic species, the radius decreases as the nuclear charge increases. Clear? And the measured radii agree, in picometres. Nitrogen three minus is one hundred and seventy one, oxygen two minus is one hundred and forty, fluorine minus is one hundred and thirty six, sodium plus is one hundred and two, magnesium two plus is seventy two, and aluminium three plus is fifty four. So our puzzle is solved: the same ten electrons, but thirteen protons pull much harder than seven. Got it?

3:59Trap: count the electrons first

Now, a trap that catches many students. Compare oxygen two minus and sulphur two minus. Sulphur has sixteen protons, and oxygen only eight. Higher nuclear charge, so sulphur two minus must be smaller, right? Oh no, careful, that is exactly the trap! Count the electrons first. Oxygen two minus has ten electrons, but sulphur two minus has eighteen. Okay? So these two are not isoelectronic, and the nuclear charge rule simply does not apply here. Right? Instead, we use the group trend. Oxygen and sulphur sit in the same group, and going down a group adds a new shell. So sulphur two minus is larger than oxygen two minus. Remember, the nuclear charge rule works only when the electron counts are equal. Clear?

4:50Example 1: order S2-, Cl-, K+, Ca2+ by decreasing radius

Now, example one. Arrange sulphur two minus, chlorine minus, potassium plus and calcium two plus in decreasing order of radius, which means the largest first. Pause the video and try it first. Done? Okay, let's check. Before we order anything, what is the very first thing we check? The number of electrons, exactly! Sulphur has sixteen, and two more gives eighteen. Chlorine has seventeen, and one more gives eighteen. Potassium has nineteen, and one less gives eighteen. Calcium has twenty, and two less gives eighteen. With me? So all four are isoelectronic, with eighteen electrons each, and the nuclear charge decides. Here Z is sixteen, seventeen, nineteen and twenty. The highest nuclear charge pulls the hardest, so it gives the smallest ion. Okay? So the order is sulphur two minus, greater than chlorine minus, greater than potassium plus, greater than calcium two plus. The two anions are the largest, and calcium two plus, with twenty protons, is the smallest. Very good, you got the method!

5:59Example 2: order Li+, Mg2+, Be2+, Na+ by increasing radius

Now a slightly harder one. Arrange lithium plus, magnesium two plus, beryllium two plus and sodium plus in increasing order of radius, which means the smallest first. Pause the video and try it. Here is a hint: look for the isoelectronic pairs. Done? Okay, let's check. Lithium plus and beryllium two plus have two electrons each. Sodium plus and magnesium two plus have ten electrons each. So we have two isoelectronic pairs. Okay? Now use the rule we just learnt. Inside each pair, which ion is the smaller one? The one with the higher nuclear charge, yes! Beryllium has four protons and lithium has three, so beryllium two plus is smaller than lithium plus. The less than sign on screen means a smaller radius. In the same way, magnesium two plus is smaller than sodium plus. Right? Now the tricky part: lithium plus or magnesium two plus? Lithium plus has only one shell of electrons, and magnesium two plus has two shells. So lithium plus must be the smaller one, right? Oh no, careful, the actual radii say otherwise! Look at the radii in picometres. Beryllium two plus is thirty one, magnesium two plus is seventy two, lithium plus is seventy six, and sodium plus is one hundred and two. So magnesium two plus, at seventy two, is a little smaller than lithium plus, at seventy six. Clear? So the increasing order is beryllium two plus, less than magnesium two plus, less than lithium plus, less than sodium plus. Got it? And notice how close lithium plus and magnesium two plus are, at seventy six and seventy two picometres. This is the diagonal relationship between lithium and magnesium, and you will meet it again later in this unit. Very good, well done!

7:56Quick revision: cation, anion and isoelectronic sizes

So, quick revision. The cation is smaller than its atom, and the anion is larger; and for iron, the higher the charge, the smaller the ion. Among isoelectronic species, the radius falls as the nuclear charge rises. And always count the electrons first: sulphur two minus and oxygen two minus are not isoelectronic, so we use the group trend, and sulphur two minus is larger. Now go and try the practice problems on this page. All the best!