To determine the diameter of an oil molecule using the given information, we can follow these steps:
1. Calculate the area of the oil slick:
- The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius.
- In this case, the radius is given as 41.8 cm, so we need to convert it to meters by dividing by 100 (since 1 meter = 100 cm).
- Calculate the area using the formula: A = π(41.8/100)^2.
2. Estimate the number of oil molecules in the oil slick:
- Since the slick is approximately one molecule thick, the number of molecules can be approximated by dividing the mass of the droplet by the mass of a single molecule.
- The density of the oil is given as 1174 kg/m^3, which gives us the mass/volume ratio.
- So, the volume of the droplet can be calculated as V = M / ρ, where M is the mass of the droplet and ρ is the density of the oil.
- Calculate the volume of the droplet using the given values.
- Based on the assumption that the droplet has formed a slick that is one molecule thick, the volume of the droplet can be considered to be equal to the volume of the slick.
- Divide the volume of the slick by the volume of a single oil molecule to estimate the number of oil molecules in the slick.
3. Calculate the diameter of the oil molecule:
- The diameter of a sphere can be calculated using the formula D = 2√(V/π), where D represents the diameter and V is the volume of the molecule.
- Divide the volume of a single oil molecule by the number of oil molecules calculated in the previous step.
- Calculate the square root of this value.
- Multiply the square root by 2 to obtain the diameter of the oil molecule.
By following these steps and plugging in the given values, you can calculate the diameter of an oil molecule.