Final answer:
To find the average thickness of a sheet of gold leaf, one must use the mass and density of gold to calculate the volume, and then divide by the area in cm2, obtained from the length and width of the sheet in inches converted to centimeters. The final thickness can be converted to meters for the final answer.
Step-by-step explanation:
To calculate the average thickness of the gold leaf, we need to use the density formula which relates mass, volume, and density. For gold, density (d) is written as d = 19.3 g/cm3. By rearranging the density formula, we can solve for the volume (V) using the mass (m) of the gold piece which is V = m/d.
The mass of the gold piece is 330 mg, or 0.33 g (since 1000 mg = 1 g). Using the density of gold, the volume is calculated as: V = 0.33 g / 19.3 g/cm3 = 0.0171 cm3. We then convert the length and width from inches to centimeters: length of 2.07 in equals 5.258 cm and width of 2.28 in equals 5.7912 cm.
Now, to find the thickness (t), we use the volume of a rectangular prism (V = length × width × thickness). So, t = V / (length × width) = 0.0171 cm3 / (5.258 cm × 5.7912 cm).
After calculating, we find t = 0.000532 cm or 5.32 x 10-6 m since 1 cm = 0.01 m.