Avogadro\'s number can be computed from the following measured properties of pur

Question

Avogadro's number can be computed from the following measured properties of pure crystalline silicon: atomic mass (obtained from the mass and abundance of each isotope), density of the crystal, size of the unit cell (the smallest repeating unit in the crystal), and number of atoms in the unit cell. For the material that was used, the average atomic mass of Si is m_si = 28.0853842 (35) g/mol, where 35 is the uncertainty (standard deviation) in the last two digits. The density is rho = 2.3290319 (18) g/cm^3, the size of the cubic unit cell is c_o = 5.43102036 (33) Times 10^-8 cm, and there are 8 atoms per unit cell. Avogadro's number is computed from the equation below. From the measured properties and their uncertainties, compute Avogadro's number and its uncertainty. To find the uncertainty of c_o^3, use the function y = x^a in the rules for propagation of uncertainty table.

Explanation / Answer

ANSWER:

Calculte the % uncertainties in individual measurements and then add these. The sum if individual % uncetanties is the uncertainty in final answer

% Uncertainty im msi = (Uncetainty / Value of quantity) X 100 = (0.0000035 / 28.0853842) = 0.000018%

% Uncertainty im = (0.0000018 / 2.3290319) X 100 = 0.000077%

% Uncertainty im c = 3 X % uncetainty

% Uncertainty im c = 3 X (0.00000033 / 5.43102036) X 100 = 0.000018%

total uncertainty = 0.000018 + 0.000077 + 0.000018 = 0.000113%

Na = msi / ( c3)/8 = 28.0853842 / (2.3290319 X 5.43102036 X 10-8)3 / 8 = 1.110196241 X 1023

% uncetanty = 0.000113

Na = 1.110196241 X 1023 +(-) 0.000113%

Na = 1.1101949865 X 1023 +(-) 0.0000012545

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