Final answer:
To find the thickness of the nickel sheet, the volume is calculated using the mass and density, and then divided by the area of the sheet. The thickness is approximately 0.011236 mm.
Step-by-step explanation:
To calculate the thickness of a thin sheet of nickel given its dimensions, weight, and the density of nickel, we start by using the formula for density \( \rho = \frac{m}{V} \), where \( \rho \) is the density, m is mass, and V is volume. The thickness can be found by rearranging the formula for volume, V = area \( \times \) thickness, and solving for thickness using the given mass and density.
The sheet has dimensions of 5.00 cm by 7.00 cm, so the area, A, is A = 5.00\,cm \times 7.00\,cm = 35.00\,cm^2. Given the mass of the nickel sheet is 0.350 g and the density of nickel is 8.90 g/cm3, we use the density formula to find volume:
\( \rho = \frac{m}{V} \Rightarrow V = \frac{m}{\rho} = \frac{0.350\,g}{8.90\,g/cm^3} = 0.0393258\,cm^3 \).
Now we solve for thickness:
Volume = Area \( \times \) Thickness \( \Rightarrow \) Thickness = Volume / Area = 0.0393258\,cm3 / 35.00\,cm2 = 0.0011236\,cm, or 0.011236\,mm.
The thickness of the nickel sheet is therefore approximately 0.011236 mm.