|__|___|
The vertical lines represent the center of the left cation, the anion, and the right cation. This is the way I envision it from the problem. Draw a small circle around the left vertical line, a small circle around the right vertical line, and a large circle around the middle vertical line. The problem says they are lying next to each other; I'm assuming this means they touch although it doesn't say that exactly. I don't know how to work the problem if they don't touch. So you have two unknowns and you need two equations.
Let C = the cation radius.
Let A = the anion radius.
We know the center to center distance for the cations is 587 pm and we know the center line passes through the center of the anion. Therefore,
2C + 2A = 587
The second equation we know is that
C = 0.551 A
Solve the two equations simultaneously and solve for C and A. Post your work if you get stuck. Check my thinking.
I need help with getting started:
1.The crystal structure of an ionic compound consists of alternating cations and anions lying next to each other in three dimensions. If the cation radius is 55.1% of the anion radius and the distance between the cation nuclei is 587 pm, what are the radii of the two ions? (Note: This ionic compound is a three dimensional array. The cation to cation, center-to-center distance specified is through the center of the anion.)
1 answer