Calculating radius of Rubidium in unit cellHelp.

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Discussion Overview

The discussion revolves around calculating the radius of the Rubidium ion in a unit cell of Rubidium chloride, which adopts a sodium chloride structure. Participants explore the relationship between density, unit cell dimensions, and ionic radii, while addressing uncertainties in the calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to find the radius without knowing any length, assuming the density refers to the entire unit cell.
  • Another participant inquires about the number of moles of RbCl per cubic centimeter and how this relates to the number of molecules and unit cells.
  • It is noted that there are 4 moles of sodium and 4 chloride units in one unit cell, although a later reply corrects this to refer to atoms instead of moles.
  • One participant suggests that knowing the radii ratio might be necessary, although it is not provided in the problem.
  • Another participant reflects on the challenge of calculating the radius, acknowledging that while the sum of the cation and anion radii is clear, separating them remains uncertain.
  • It is mentioned that the radii of the ions are almost identical, but this is not specified in the question.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to calculate the radius of the Rubidium ion, with multiple competing views and uncertainties remaining throughout the discussion.

Contextual Notes

There are limitations regarding assumptions about the density, the relationship between moles and unit cells, and the lack of specific information on the radii ratio.

christian0710
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Homework Statement



Calculate the Radius of Rubidium ion (which adopts sodium chloride structure.), if the density of Rubidium chloride is 2.76g*cm^(-3) and if we assume that the ions touch each other along the sides of the edge of the unit cell.


I'm a bit lost here. I assume the density is the density of the whole unit cell. But how can I find a radius without knowing any length at all?
 
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How many moles of RbCl per one cubic centimeter of the crystal? How many molecules it is? Unit cells?
 
In one unit cell there must be 4 moles of sodium and 4 chloride units even thought the cation sodium is much smaller than Cl.
 
christian0710 said:
In one unit cell there must be 4 moles of sodium

Atoms, not moles. And mole is known number of atoms (molecules, ions, whatever).
 
Ahh yes, so perhaps if we know the radii ratio? It's not given in the problem, but i could imagine we would have to know how many times one atom is bigger than another?
 
On the second thought, while apparently mole step is necessary to calculate volume of the unit cell, I don't see how to calculate radius. Sum of radii of the cation and the anion is obvious, but separating them is not, unless I am missing something.

It happens that the radii are almost identical, but it is not said in the question.
 

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