Converting Units to Find Density of Unit Cell

In summary, the atomic mass unit is defined as 1/12 the mass of an atom of carbon-12 and is equal to 1 gram per Avogadro's number. This conversion factor is used to find the density of a unit cell in grams per cubic centimeter.
  • #1
i_love_science
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I don't understand the ratio [ 1 g / 6.02*10^23 amu] in the following conversion factor:

[228.2 amu / 4.75*10^(-23) cm3] * [ 1 g / 6.02*10^23 amu] = 7.98 g/cm3

(This calculation is in a problem where you're finding the density of a unit cell in g/cm3 - though it has nothing to do with the conversion factor itself)

Thanks.
 
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  • #2
The atomic mass unit ##m_u## is defined as ##1/12## the mass of an atom of ##^{12}C##. Also, a mole is the number ##^{12}C## atoms in ##12\text{g}## of ##^{12}C## ##\implies## the mass of an individual ##^{12}C## atom is ##\mathrm{12g}/N_A## and the atomic mass unit is ##m_u = \mathrm{1g}/N_A##. It follows that$$\frac{1\text{g}}{6.02 \times 10^{23} m_u} = 1$$
 

1. What is the formula for finding the density of a unit cell?

The formula for finding the density of a unit cell is mass divided by volume. This can be represented as D = m/V, where D is density, m is mass, and V is volume.

2. How do you convert units for mass and volume when finding density of a unit cell?

To convert units for mass, you can use the conversion factor of 1 gram = 1000 milligrams. For volume, the conversion factor is 1 cubic centimeter = 1000 cubic millimeters. You can also use online unit conversion calculators for more complex conversions.

3. What units are commonly used for density of a unit cell?

The most commonly used units for density of a unit cell are grams per cubic centimeter (g/cm3) and kilograms per cubic meter (kg/m3). However, other units such as pounds per cubic inch (lb/in3) and grams per milliliter (g/mL) may also be used.

4. How does the density of a unit cell relate to its structure?

The density of a unit cell is directly related to its structure. A unit cell with a more compact structure will have a higher density, while a unit cell with a less compact structure will have a lower density. This is because a more compact structure means there is less empty space between particles, resulting in a higher mass per unit volume.

5. Can the density of a unit cell be used to identify a substance?

Yes, the density of a unit cell can be used to identify a substance. Each substance has a unique density, so by comparing the density of a unit cell to known values, you can determine the substance. However, other properties such as melting point and boiling point should also be considered for a more accurate identification.

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