I have a problem that I need help with. The diameter of the oil molecule has to be calculated and presented in scientific notation. The data in the questions tells me that drop of oil(volume 0.05cm ^3) is released from a dropper onto the surface of the water.The film of oil has the thickness of the diameter of an oil molecule.

Question

I have a problem that I need help with. The diameter of the oil molecule has to be calculated and presented in scientific notation. The data in the questions tells me that drop of oil(volume 0.05cm ^3) is released from a dropper onto the surface of the water.The film of oil has the thickness of the diameter of an oil molecule.

The volume of the oil is thickness* area of film.

set that equal to the volume of the drop, given, and solve for thickness.

thank you Bob, I will try this and see how I get on.

Answer 1

You're welcome! I'm here to help you out. Let's solve the problem step by step.

First, we need to find the area of the film of oil. Since the oil drop spreads out to form a circular film, we can assume the film has a circular shape. The area of a circle can be calculated using the formula:

Area = π * radius^2

However, in this case, we don't know the radius directly. Instead, we need to find the thickness of the film, which is the same as the diameter of an oil molecule.

Let's call the diameter/thickness of the oil molecule "d". So, the radius of the film would be half of the thickness: r = d/2.

So, the formula for the area of the film becomes:

Area = π * (d/2)^2

Next, the volume of the oil can be obtained by multiplying the thickness (d) by the area of the film. Therefore, the volume of the oil is:

Volume of oil = d * π * (d/2)^2

Now, given that the volume of the oil drop is 0.05 cm^3, we can set up the equation:

0.05 = d * π * (d/2)^2

To find the diameter/thickness, we need to solve this equation for "d".

Step 1: Simplify the equation

0.05 = d * π * (d^2/4)

Step 2: Simplify further

0.05 = (π/4) * d^3

Step 3: Divide both sides of the equation by (π/4) to isolate d^3

0.05 / (π/4) = d^3

Step 4: Solve for d by taking the cube root of both sides

d = (0.05 / (π/4))^(1/3)

Now, evaluate this expression on a calculator to get the value of d. Keep in mind that when presenting the diameter in scientific notation, you should write it as a number between 1 and 10 multiplied by a power of 10.

I hope this helps! Let me know if you have any further questions.