# Density of chromium ions in ruby

1. Mar 10, 2016

### lcr2139

1. The problem statement, all variables and given/known data
estimate the density of chromium ions in ruby, assuming that the concentration of chromium in ruby is about 0.05% by weight.

2. Relevant equations
decay rate = 0.5x10^3 s^-1
answer: density N (sub T)= 1.6x10^19 cm^-3

3. The attempt at a solution
density = mass/volume
density of ruby = 4.02 g/cm^3
density of chromium = (4.02)(0.05) = .201 g/cm^3
I know that this is wrong!
What do I do?

2. Mar 10, 2016

### haruspex

It says "0.05%". Did you mean that or 5%?

3. Mar 12, 2016

### lcr2139

Yes, I really meant 0.05%.

4. Mar 12, 2016

### haruspex

But your calculation treated it as 5%.
I believe you will also need the atomic mass of chromium.

5. Mar 13, 2016

### ChuckB

0.5*10^-3 = .0005 which = .05%

lcr2139 treated it properly in the calculation (not to say that I have any idea what the calculation is, only that I know that 0.5*10^-3 = .05%)

6. Mar 13, 2016

### haruspex

The 0.5*10-3 was quoted as a decay rate, with the right units for that, which has nothing to do with the problem. (In fact, lcr wrote 103, not 10-3., but minus seems more likely for a decay rate.)
In the calculation, lcr used 5% here:

Last edited: Mar 13, 2016
7. Mar 13, 2016

### lcr2139

density of ruby: 4.02 g/cm^3
molecular weight of chromium: 52 g/mol

(4.02g/cm^3)*(.0005)*(6.022*10^23 atoms/mol) / (52 g/mol) = 2.32*10^19 cm^-3

This is wrong! The real answer is NsubT= 1.6 * 10^19 cm^-3

where am I going wrong?

8. Mar 13, 2016

### haruspex

Your calculation looks right to me.