Question

One crystalline form of silica (SiO2) has a cubic unit cell, and from X-ray diffraction data it is known that the cell edge length is 0.700 nm. If the measured density is 2.32 g/cm3, how many (a) Si4 and (b) O2- ions are there per unit cell

Answer 1

There are 8Si atoms and 16 O atoms per unit cell

Step-by-step explanation:

From the question we are told that:

Edge length
`l=0.700nm=>0.7*10^9nm`

Density
`\rho=2.32g/cm^3`

Generally the equation for Volume is mathematically given by

`V=l^3`

`V=(0.7*10^9)m^3`

`V=3,43*10^-{22}cm`

Where

Molar mass of (SiO2) for one formula unit

`M=28+32`

`M=60g/mol`

Therefore

Density of Si per unit length is

`\rho_(si)=(9.96*10^(23))/(3.43*10^22)`

`\rho=0.29`

Molar mass of (SiO2) for one formula unit

`M=28+32`

`M=60g/mol`

Therefore

There are 8Si atoms and 16 O atoms per unit cell