Question

A kimberlite pipe has a bulk density of 2.5 g/cc and contains diamond of grade 100 carat/metric ton. If the pipe contains only 1-carat diamond crystals, then the number of diamond crystals per cubic meter in the pipe is .................. (In integer)

Hint:

To find the number of crystals, first convert the bulk density to kg/m³, then multiply by the grade and divide by the weight of each crystal.

Answer 1

Step 1: Calculate the mass of diamond per cubic meter.
The bulk density is given as 2.5 g/cc, and we convert this to kg/m³. Since \(1 \, \text{g/cc} = 1000 \, \text{kg/m}^3\), we have: \[ \text{Bulk density} = 2.5 \, \text{g/cc} = 2500 \, \text{kg/m}^3 \] Step 2: Determine how many carats are there in 1 metric ton.
1 metric ton = 1000 kg. Since the grade is 100 carats per metric ton, there are: \[ 100 \, \text{carats} \, \text{per} \, 1000 \, \text{kg}. \] Step 3: Calculate the number of carats per cubic meter.
The number of carats per cubic meter is: \[ \frac{2500 \, \text{kg/m}^3}{1000} \times 100 = 250 \, \text{carats/m}^3 \] Step 4: Find the number of diamond crystals per cubic meter.
Since each diamond crystal is 1 carat, the number of crystals per cubic meter is the same as the number of carats: \[ \boxed{250} \] Final Answer: \[ \boxed{250} \]