Question

Compute the atomic density (the number of atoms per cm3 rather than mass density g/cm3) for a perfect crystal of silicon at room temperature, given that the room temperature density and atomic weight of silicon are 2.33 g/cm3 and 28.09 g/mol, respectively.

Hint: you do NOT need any information about the crystal structure of silicon to solve for this quantity, based on the information provided in this particular problem.
Be sure to use values exactly as given and do not round until the final answer.
Use 6.022x1023 , exactly, for Avogadro's Number.
Answer Format: XEX where EX stands for *10x
Units: atoms/cm3
Example: So for an answer of 158123.126 you would type: 2E5 since only a whole number is prescribed for the prefix.

Answer 1

5E22 atoms/cm³

Step-by-step explanation:

We need to find the number of moles of silicon per cm³

number of moles per cm³ = density/atomic weight = 2.33 g/cm ÷ 28.09 g/mol = 0.083 mol/cm³.

Since there are 6.022 × 10²³ atoms/mol, then the number of atoms of silicon per cm³ = number of atoms per mol × number of moles per cm³

= 6.022 × 10²³ atoms/mol × 0.083 mol/cm³

= 0.4995 × 10²³ atoms/cm³

= 4.995 × 10²² atoms/cm³

≅ 5 × 10²² atoms/cm³

= 5E22 atoms/cm³