Question

A ruby crystal has a composition (Al0.99Cr0.01)2O3. How many Cr3þ ions are there in a ruby of dimensions 1 cm3 ? (The unit cell dimensions are a ¼ 0.4763 nm, c ¼ 1.3009 nm; Z (the unit cell contents) ¼ 6Al2O3; the volume of the unit cell can be taken as 0.966a 2 c.)

Answer 1

To determine the number of Cr³+ ions in a ruby crystal of dimensions 1 cm³, we need to calculate the number of formula units in the crystal.

Step-by-step explanation:

To determine the number of Cr³+ ions in the ruby crystal, we need to calculate the number of formula units in a 1 cm³ ruby crystal. First, we need to calculate the volume of the unit cell using the given unit cell dimensions. The volume of the unit cell can be calculated as follows:

Volume of the unit cell = 0.966a²c = 0.966(0.4763 nm)²(1.3009 nm) = 0.2376 nm³

Next, we need to calculate the number of unit cells in 1 cm³ crystal:

Number of unit cells = (1 cm³) / (0.2376 nm³) = 4207.983

Since the formula unit Al₂O₃ contains 2 Al atoms, the number of Cr³+ ions can be calculated as follows:

Number of Cr³+ ions = (0.01 x 4207.983) / 6 = 7.013

Therefore, there are approximately 7 Cr³+ ions in a ruby crystal of dimensions 1 cm³.