The density of SiC(Silicon Carbide) is 3.21 g/ml and that of diamond is 3.51g/ml.The shortest distance between any two carbon atoms in diamond is 154 picometres(pm) .Find atomic radius of Si in SiC

To find the atomic radius of silicon in silicon carbide (SiC), we can use the information provided about the densities of SiC and diamond, along with the distance between carbon atoms in diamond. Let's break this down step by step.

Understanding the Structure of SiC

Silicon carbide is a compound made up of silicon and carbon atoms. In its crystalline form, SiC has a structure where silicon atoms are bonded to carbon atoms in a tetrahedral arrangement. This means that each silicon atom is surrounded by four carbon atoms, and vice versa.

Using Density to Find Molar Mass

First, we need to relate the density of SiC to its molar mass. The formula for density is:

• Density (ρ) = Mass (m) / Volume (V)

We can rearrange this to find the mass of one mole of SiC:

• Mass = Density × Volume

Given that the density of SiC is 3.21 g/ml, we can convert this to g/cm³ (since 1 ml = 1 cm³), which remains 3.21 g/cm³. The molar volume of a substance can be calculated using the molar mass and density:

• Molar Volume = Molar Mass / Density

Calculating Molar Mass of SiC

To find the molar mass of SiC, we need to consider the atomic masses of silicon (Si) and carbon (C). The atomic mass of silicon is approximately 28.09 g/mol, and that of carbon is about 12.01 g/mol. Therefore, the molar mass of SiC can be calculated as follows:

• Molar Mass of SiC = Atomic Mass of Si + Atomic Mass of C
• Molar Mass of SiC = 28.09 g/mol + 12.01 g/mol = 40.10 g/mol

Finding the Molar Volume

Now, we can calculate the molar volume of SiC using its density:

• Molar Volume = Molar Mass / Density = 40.10 g/mol / 3.21 g/cm³ ≈ 12.50 cm³/mol

Relating Atomic Radius to Atomic Arrangement

In the crystal structure of SiC, each silicon atom is tetrahedrally coordinated by four carbon atoms. The distance between the silicon and carbon atoms can be estimated based on the bond lengths in the structure. However, we need to find the atomic radius of silicon specifically.

Using Carbon-Carbon Distance

The shortest distance between two carbon atoms in diamond is given as 154 picometers (pm). In a tetrahedral structure, the distance between the silicon atom and the carbon atoms can be approximated. The bond length between Si and C in SiC is typically around 1.89 Å (189 pm).

Calculating the Atomic Radius of Silicon

To find the atomic radius of silicon, we can use the bond length between silicon and carbon. Since the bond length is the distance from the center of one atom to the center of another, we can estimate the atomic radius of silicon as follows:

• Atomic Radius of Si ≈ Bond Length (Si-C) / 2
• Atomic Radius of Si ≈ 189 pm / 2 ≈ 94.5 pm

Final Thoughts

Thus, the atomic radius of silicon in silicon carbide is approximately 94.5 picometers. This value is consistent with the typical atomic radii observed for silicon in various compounds. Understanding these relationships helps in grasping the properties and behaviors of materials like SiC in various applications, from electronics to abrasives.