How many protons are contained in a circular puddle of mercury that is 8.5 inches wide and .25 inches deep?
To determine the number of protons in a circular puddle of mercury, we need to calculate the volume of the puddle and then use Avogadro's number to convert it into the number of atoms or protons. Here's how you can do it:
Step 1: Calculate the volume of the puddle.
The volume of a cylinder (which the puddle resembles) can be calculated using the formula: V = πr^2h, where V is the volume, r is the radius, and h is the height or depth of the cylinder.
Given:
- Radius (r) = 8.5 inches / 2 = 4.25 inches
- Depth (h) = 0.25 inches
Using the formula, plug in the values:
V = π(4.25 inches)^2 * 0.25 inches
V ≈ 14.047 cubic inches
Step 2: Convert the volume to units of liters.
Since Avogadro's number is based on the SI unit (mole), it's necessary to convert the volume from cubic inches to liters. There are 61.024 cubic inches in 1 liter.
Conversion: 14.047 cubic inches * (1 liter / 61.024 cubic inches)
≈ 0.230 liters
Step 3: Use Avogadro's number to convert to the number of atoms or protons.
Avogadro's number (represented by the symbol NA) is approximately 6.022 x 10^23. This number refers to the number of atoms or particles in one mole of a substance.
To calculate the number of protons, we need to know the molar mass or atomic weight of mercury. The molar mass of mercury is 200.59 g/mol.
Given:
- Volume (V) = 0.230 liters
- Molar mass (M) = 200.59 g/mol
Now, we can use the formula: Number of Protons = (V * NA) / M
Substituting the values:
Number of Protons = (0.230 liters * 6.022 x 10^23 particles/mol) / 200.59 g/mol
Calculating the answer will yield the number of protons in the circular puddle of mercury.
What's the size of the protons? You can look up the diameter and the area of a sphere (if you assume they are spheres) is (4/3)*pi*4^3. Do you want the Hg in cubic inches or cubic centimeters. If cc, then
8.5 in x (2.54 cm/in) = ? cm
Area of Hg is pi*r^2
thickness is 0.25 in and that is
0.25 in x (2.54 cm/in) = ?