Density of chromium ions in ruby

[lcr2139]

Homework Statement

estimate the density of chromium ions in ruby, assuming that the concentration of chromium in ruby is about 0.05% by weight.

Homework Equations

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

 

[haruspex]

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

 

[lcr2139]

Yes, I really meant 0.05%.

 

[haruspex]

Yes, I really meant 0.05%.

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

 

[ChuckB]

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

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%)

 

[haruspex]

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%)

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:

density of ruby = 4.02 g/cm^3
density of chromium = (4.02)(0.05) = .201 g/cm^3

 

[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?

 

[haruspex]

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?

Your calculation looks right to me.