Estimate the fraction of of unoccupied atomic sites in lead (Pb) at a temperature 10K below its melting point.
DATA:
Vacancy Fraction, nv/N T (degrees C)
1.8*10-7 100
7.2*10-6 200
Express your answer in terms of vacancy fraction, nv/N:
1*10^-4
1e-4
To estimate the fraction of unoccupied atomic sites in lead (Pb) at a temperature 10K below its melting point, we can use the given data points. The data provides the vacancy fraction, nv/N, at different temperatures.
First, let's convert the given temperature of 10K below the melting point to degrees Celsius. We know that the melting point of lead is approximately 327.5 degrees Celsius. Therefore, 10K below the melting point would be 327.5 - 10 = 317.5 degrees Celsius.
Now, we need to find the vacancy fraction, nv/N, at 317.5 degrees Celsius. However, we don't have the exact data point for this temperature. To estimate the fraction, we can use interpolation.
Interpolation is a method of estimating a value between two known values by examining the known data points. In this case, we can estimate the vacancy fraction at 317.5 degrees Celsius by interpolating between the two nearest data points, which are 1.8*10^-7 at 100 degrees Celsius and 7.2*10^-6 at 200 degrees Celsius.
To interpolate, we can use the formula:
Fraction = Fraction1 + (Fraction2 - Fraction1) * (Temperature - Temperature1) / (Temperature2 - Temperature1)
Let's plug in the values:
Fraction1 = 1.8*10^-7
Fraction2 = 7.2*10^-6
Temperature1 = 100
Temperature2 = 200
Temperature = 317.5
Fraction = 1.8*10^-7 + (7.2*10^-6 - 1.8*10^-7) * (317.5 - 100) / (200 - 100)
Using this formula, we can calculate the estimated fraction of unoccupied atomic sites in lead at 317.5 degrees Celsius.