Question

Phosphorus crystallizes in several different forms, one of which is a simple cube with an edge length of 238 pm. What is the density of phosphorus in the simple cubic crystal form?

Answer 1

Answer: The density of phosphorus is
`3.81g/cm^3`

Step-by-step explanation:

To calculate the density of phosphorus, we use the equation:

`\rho=(Z* M)/(N_(A)* a^(3))`

where,

`\rho` = density

Z = number of atom in unit cell = 1 (CCP)

M = atomic mass of phosphorus = 31 g/mol

`N_(A)` = Avogadro's number =
`6.022* 10^(23)`

a = edge length of unit cell =
`238pm=238* 10^(-10)cm` (Conversion factor:
`1cm=10^(10)pm` )

Putting values in above equation, we get:

`\rho=(1* 31)/(6.022* 10^(23)* (238* 10^(-10))^3)\\\\\rho=3.81g/cm^3`

Hence, the density of phosphorus is
`3.81g/cm^3`