Silicon for computer chips is grown in large cylinders called “boules” that are 300 mm in diameter and 2 m in length,as shown.(Figure 1) The density of silicon is 2.33 g/cm3. Silicon wafers for making integrated circuits are sliced from a 2.0 m boule and are typically 0.75 mm thick and 300. mm in diameter.

Silicon for computer chips is grown in large cylinders called “boules” that are 300 mm in diameter and 2 m in length,as shown.(Figure 1) The density of silicon is 2.33 g/cm3. Silicon wafers for making integrated circuits are sliced from a 2.0 m boule and are typically 0.75 mm thick and 300. mm in diameter. How many wafers can be cut from a single boule

2.7

To find the volume of the 2.0 m boule, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

where π is a constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.

Given:
Diameter of the boule = 300 mm
Radius of the boule = diameter / 2 = 300 mm / 2 = 150 mm = 15 cm
Height of the boule = 2 m = 200 cm

Substituting these values into the formula:

Volume = π * (15 cm)^2 * 200 cm
Volume ≈ 3.14159 * 225 cm^2 * 200 cm
Volume ≈ 3.14159 * 45,000 cm^3
Volume ≈ 141,371 cm^3

Now, let's find the mass of silicon in the boule:

Mass = Volume * Density

Given:
Density of silicon = 2.33 g/cm^3

Substituting the values:

Mass = 141,371 cm^3 * 2.33 g/cm^3
Mass ≈ 329,835.43 g

To find the volume of a silicon wafer, we can simply use the formula for the area of a circle:

Area = π * r^2

Given:
Diameter of the wafer = 300 mm
Radius of the wafer = diameter / 2 = 300 mm / 2 = 150 mm = 15 cm

Substituting these values into the formula:

Area = π * (15 cm)^2
Area ≈ 3.14159 * 225 cm^2
Area ≈ 706.86 cm^2

To find the mass of the wafer, we can use the formula:

Mass = Volume * Density

Given:
Thickness of the wafer = 0.75 mm = 0.075 cm

Substituting the values:

Volume = Area * Thickness
Volume ≈ 706.86 cm^2 * 0.075 cm
Volume ≈ 53.01 cm^3

Mass = Volume * Density

Given:
Density of silicon = 2.33 g/cm^3

Substituting the values:

Mass = 53.01 cm^3 * 2.33 g/cm^3
Mass ≈ 123.63 g

So, the mass of the silicon wafer is approximately 123.63 grams.

To find the mass of a cylindrical boule, we can use the formula:

Mass = Volume x Density

First, let's calculate the volume of the boule:

Volume = π x (Radius^2) x Length

Given that the diameter of the boule is 300 mm, the radius would be half of that, which is 150 mm or 15 cm. The length of the boule is given as 2 m or 200 cm.

Plugging in these values, we have:

Volume = π x (15 cm)^2 x 200 cm
= π x 225 cm^2 x 200 cm
= 225π x 200 cm^3
= 45,000π cm^3

Now, let's calculate the mass of the boule by multiplying the volume by the density:

Mass = 45,000π cm^3 x 2.33 g/cm^3
= 104,850π g

To find the mass of a silicon wafer, we can use the same formula:

Mass = Volume x Density

Since the wafer is a circular disk, the volume can be calculated using the formula for the volume of a cylinder:

Volume = π x (Radius^2) x Thickness

Given that the diameter of the wafer is 300 mm, the radius would be half of that, which is 150 mm or 15 cm. The thickness of the wafer is given as 0.75 mm or 0.075 cm.

Plugging in these values, we have:

Volume = π x (15 cm)^2 x 0.075 cm
= π x 225 cm^2 x 0.075 cm
= 16.875π cm^3

Now, let's calculate the mass of the wafer by multiplying the volume by the density:

Mass = 16.875π cm^3 x 2.33 g/cm^3
= 39.280625π g

So, the mass of a silicon boule that is 2 m long and 300 mm in diameter is approximately 104,850π grams. And the mass of a silicon wafer that is 0.75 mm thick and 300 mm in diameter is approximately 39.280625π grams.