Arrange the following in order of increasing ionic radius: I^-, Cs+, and Te^2-. Explain this order

To arrange the ions I^-, Cs+, and Te^2- in order of increasing ionic radius, we need to consider the concept of effective nuclear charge and electron-electron repulsion.

The effective nuclear charge (Zeff) is the net positive charge experienced by an electron in an atom or ion. It is determined by subtracting the number of core electrons (non-valence electrons) from the total number of protons in the nucleus.

When comparing ions, the ionic radius generally increases as we move down a group in the periodic table and decreases as we move across a period from left to right.

Now, let's analyze the three ions given:

1. I^- (Iodide ion): Iodine (I) is in Group 7 (also known as Group 17 or the halogens) of the periodic table. It has 53 electrons and belongs to Period 5. When iodine gains one electron to form the iodide ion (I^-), it has a stable octet arrangement (completing its outer electron shell). Since iodine is located towards the top of Group 7, the effective nuclear charge is relatively high, pulling the outermost electron closer to the nucleus. Thus, I^- has the smallest ionic radius among the given ions.

2. Cs+ (Cesium ion): Cesium (Cs) is in Group 1 of the periodic table. It has 55 electrons and belongs to Period 6. When cesium loses one electron to form the cesium ion (Cs+), it becomes a positively charged ion with a stable electron configuration. Cesium is located at the bottom of Group 1, so the effective nuclear charge is lower, and the outermost electron is farther away from the nucleus. As a result, Cs+ has a larger ionic radius compared to I^-.

3. Te^2- (Telluride ion): Tellurium (Te) is in Group 16 (also known as Group 6A) of the periodic table. It has 52 electrons and belongs to Period 5. When tellurium gains two electrons to form the telluride ion (Te^2-), it completes its outer electron shell and achieves a stable configuration. The effective nuclear charge acting on the outermost electron is higher in telluride ion compared to iodide ion, but lower compared to cesium ion. Hence, Te^2- has an intermediate ionic radius.

Therefore, arranging the ions in increasing ionic radius, we have:

I^- < Te^2- < Cs+