The unit cell for cr2o3 has hexagonal symmetry with lattice parameters a = 0.4961 nm and c = 1.360 nm. if the density of this material is 5.22 g/cm3, calculate its atomic packing factor. the atomic weights of cr

To calculate the packing factor, first calculate the area and volume of unit cell.

Area is calculated as:

Here, R is radius and is related to a as follows:

Putting the value in expression for area,

The value of a is 0.4961 nm

Since,

Thus,

Putting the value,

Now, volume can be calculated as follows:

The value of c is 1.360 nm or

Putting the value,

now, number of atom in unit cell can be calculated by using the following formula:

Here, A is atomic mass of is 151.99 g/mol.

Putting all the values,

Thus, there will be 18 units in 1 unit cell.

Since, there are 2 Cr atoms and 3 oxygen atoms thus, units of chromium and oxygen will be 2×18=36 and 3×18=54 respectively.

The atomic radii of and is 62 pm and 140 pm respectively.

Converting them into cm:

Thus,

and,

Volume of sphere will be sum of volume of total number of cations and anions thus,

Since, volume of sphere is ,

Putting the values,

The atomic packing factor is ratio of volume of sphere and volume of crystal, thus,

Thus, atomic packing factor is 0.758.

is there multiple choice answers?

alkaline metals are lithium, sodium, rubidium, potassium, cesium and francium.

alkali metals have electronegativity from 0.7 to 1, lowest in periodic table of elements, which means that alkali metals (i group in periodic table) has positive oxidation number in compounds.

electronegativity is a chemical property that describes the tendency of an atom to attract a shared pair of electrons towards itself.

alkaline metals (far left in main group) have lowest ionizations energy and easy remove valence electrons,

for example, potassium is the alkali metal and has a single valence electron in the outer electron shell.

electron configuration of potassium is: ₁₉k 1s²2s²2p⁶3s²3p⁶4s¹.

they can not exist alone in nature, because they are very reactive.