The proton has a radius of approximately 1.0 times 10^{ - 13} cm and a mass of 1.7 times 10^{ - 24} g. Determine the density of a proton. For a sphere V = (4/3)times pi r^3.
To determine the density of a proton, we need to understand that density is the amount of mass per unit volume.
Given:
Radius of proton, r = 1.0 × 10^(-13) cm
Mass of proton, m = 1.7 × 10^(-24) g
First, let's calculate the volume of the sphere using the formula V = (4/3)πr^3:
V = (4/3)π(1.0 × 10^(-13))^3
V ≈ 4.18 × 10^(-39) cm^3
Now, we can calculate the density using the formula density = mass/volume:
density = m / V
density = 1.7 × 10^(-24) g / (4.18 × 10^(-39) cm^3)
To simplify the units, let's convert cm^3 to m^3, and g to kg:
density = (1.7 × 10^(-24) kg) / (4.18 × 10^(-39) m^3)
To divide the quantities, we can subtract the exponents:
density = 1.7 × 10^(15-(-39)) kg/m^3
density = 1.7 × 10^(15+39) kg/m^3
density = 1.7 × 10^(54) kg/m^3
Therefore, the density of a proton is approximately 1.7 × 10^(54) kg/m^3.
To determine the density of a proton, we need to use the formula for density, which is given by:
Density = Mass / Volume
First, let's calculate the volume of the proton using the formula you provided for a sphere:
V = (4/3) * π * r^3
Given that the radius of the proton (r) is approximately 1.0 x 10^(-13) cm, we can substitute this value into the formula:
V = (4/3) * π * (1.0 x 10^(-13))^3
Now, let's calculate the volume using a calculator or a programming language that supports scientific notation:
V ≈ 4.18879 x 10^(-39) cm^3
Next, we'll substitute the mass of the proton (m) into the formula:
m = 1.7 x 10^(-24) g
Now, we can calculate the density by dividing the mass by the volume:
Density = m / V
Substituting the values:
Density = (1.7 x 10^(-24) g) / (4.18879 x 10^(-39) cm^3)
When dividing numbers written in scientific notation, we subtract the exponents:
Density = 4.06835 x 10^(14) g/cm^3
Therefore, the density of a proton is approximately 4.06835 x 10^(14) grams per cubic centimeter.
density = mass/volume
You have the mass. Calculate volume, substitute, and solve for density.