consider a random mixture of two particles,diamond and SiC.Assume all particles are spherical with a radius of 0.100mm. The mixture is 80.0 wt% diamond(density=3.51 g/ml) and 20.0 wt% SiC (density=3.23 g/ml)
a)Calculate the mass of a single particle diamond and the number of particles in 1.00 g of this mixture
b)Calculate the relative sampling standard deviation in the number of particles of each type in a sample size of 1.00g and 10.0 mg
i used sn=SQR(Npq) formula
To calculate the mass of a single particle of diamond, we can use the formula for the volume of a sphere:
Volume = (4/3) * π * (radius)^3
Given that the radius of each particle is 0.100 mm = 0.1 cm, the volume of a single diamond particle is:
Volume = (4/3) * π * (0.1 cm)^3
Next, we can calculate the mass of a single diamond particle by multiplying its volume by its density:
Mass = Volume * Density
Given that the density of diamond is 3.51 g/ml, we need to convert the volume (cm^3) to milliliters (ml):
1 ml = 1 cm^3
Now, let's calculate the mass of a single diamond particle:
Mass = Volume * Density
= [(4/3) * π * (0.1 cm)^3] * 3.51 g/ml
Similarly, we can calculate the mass of a single SiC particle using its density (3.23 g/ml) and the same formula for volume.
To calculate the number of particles in 1.00 g of the mixture, we need to consider the weight percentages of diamond and SiC.
Given that the mixture is 80.0 wt% diamond and 20.0 wt% SiC, we can calculate the mass of diamond and SiC in 1.00 g of the mixture:
Mass of diamond = 80.0 wt% * 1.00 g = 0.80 g
Mass of SiC = 20.0 wt% * 1.00 g = 0.20 g
Now, we can calculate the number of particles for each type by dividing the mass of each type by the mass of a single particle (calculated earlier).
Number of diamond particles = Mass of diamond / Mass of a single diamond particle
Number of SiC particles = Mass of SiC / Mass of a single SiC particle
For part (b), to calculate the relative sampling standard deviation in the number of particles, we can use the formula you mentioned:
sn = SQR(Npq)
Where:
N = total number of particles (in the sampled mass)
p = probability of success (probability of selecting a diamond particle or a SiC particle)
q = probability of failure (1 - p)
For a sample size of 1.00 g, we can calculate the mass of each type of particle in the sample using the weight percentages and then calculate the number of particles for each type using the same approach as earlier. Finally, we can plug the values into the formula to calculate the relative sampling standard deviation.
For a sample size of 10.0 mg, we can repeat the calculation using the weight percentages, but this time using the mass of the sample (10.0 mg) instead of 1.00 g. Again, plug the values into the formula to calculate the relative sampling standard deviation.
Please note that the formula can vary depending on the specific sampling and statistical methods used.