Use the fact that a typical proton is spherical and has a diameter of
1x10^-13 cm and a mass of 1.67x10^-24 grams, compute density of a proton.
To compute the density of a proton, we can use the formula:
Density = Mass/Volume
First, let's determine the volume of a sphere with a given diameter using the formula:
Volume = (4/3) * π * (Radius^3)
In this case, since we are given the diameter, we can calculate the radius by dividing the diameter by 2:
Radius = Diameter/2
Now, let's substitute the given values into the equations:
Diameter = 1x10^-13 cm
Mass = 1.67x10^-24 grams
π (Pi) = 3.14159
First, we need to convert the diameter from centimeters to meters to match the mass unit:
Diameter = 1x10^-13 cm = 1x10^-15 meters
Now, let's calculate the radius:
Radius = Diameter/2 = (1x10^-15 meters)/2 = 0.5x10^-15 meters
Next, let's calculate the volume:
Volume = (4/3) * π * (Radius^3) = (4/3) * 3.14159 * (0.5x10^-15 meters)^3
Volume = 4.18879 * 0.125x10^-45 cubic meters
Now, let's calculate the density:
Density = Mass/Volume = (1.67x10^-24 grams) / (4.18879 * 0.125x10^-45 cubic meters)
Density = 3.98107x10^20 grams per cubic meter
Therefore, the density of a proton is approximately 3.98107x10^20 grams per cubic meter.