Density of chromium ions in ruby

In summary: Are you sure the answer is wrong?In summary, the conversation discusses estimating the density of chromium ions in ruby, assuming a concentration of 0.05% by weight. The attempted solution calculates a density of .201 g/cm^3 but is found to be incorrect, with the correct answer being N(sub T) = 1.6 x 10^19 cm^-3. The conversation also mentions the need for the atomic mass of chromium in the calculation.
  • #1
lcr2139
62
1

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?
 
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  • #2
It says "0.05%". Did you mean that or 5%?
 
  • #3
Yes, I really meant 0.05%.
 
  • #4
lcr2139 said:
Yes, I really meant 0.05%.
But your calculation treated it as 5%.
I believe you will also need the atomic mass of chromium.
 
  • #5
haruspex said:
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%)
 
  • #6
ChuckB said:
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:
lcr2139 said:
density of ruby = 4.02 g/cm^3
density of chromium = (4.02)(0.05) = .201 g/cm^3
 
Last edited:
  • #7
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
lcr2139 said:
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.
 

What is the density of chromium ions in ruby?

The density of chromium ions in ruby is approximately 3.98 g/cm^3.

How is the density of chromium ions in ruby calculated?

The density of chromium ions in ruby is calculated by dividing the mass of chromium ions in a given volume of ruby by the volume of the ruby sample.

What factors can affect the density of chromium ions in ruby?

The density of chromium ions in ruby can be affected by temperature, pressure, and impurities in the ruby crystal structure.

What is the significance of the density of chromium ions in ruby?

The density of chromium ions in ruby is important in determining the overall quality and value of a ruby gemstone. It can also provide insight into the formation and history of the ruby.

Is the density of chromium ions in ruby consistent among all ruby gemstones?

No, the density of chromium ions in ruby can vary slightly due to natural variations in the crystal structure and impurities present in the gemstone.

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