The proton has a radius of approximately 1.0×10−13 cm and a mass of 1.7×10−24 g.
Determine the density of a proton. For a sphere V=(43)πr3.
To determine the density of a proton, we need to find its mass and volume.
Given:
Radius of proton, r = 1.0 x 10^(-13) cm
Mass of proton, m = 1.7 x 10^(-24) g
The formula for the volume of a sphere is:
V = (4/3)πr^3
Using the given values, we can calculate the volume of the proton:
V = (4/3)π(1.0 x 10^(-13))^3
Now we can substitute the calculated volume into the formula for density:
Density = Mass / Volume
Density = m / V
Density = (1.7 x 10^(-24) g) / [(4/3)π(1.0 x 10^(-13))^3]
Now we can simplify and calculate the density.
To determine the density of a proton, we need to find the mass and volume of the proton.
Given:
Radius (r) = 1.0 × 10^(-13) cm
Mass (m) = 1.7 × 10^(-24) g
We can use the formula for the volume of a sphere:
V = (4/3)πr^3
Let's calculate the volume of the proton:
V = (4/3)π(1.0 × 10^(-13))^3
= (4/3) × 3.14 × (1.0 × 10^(-13))^3
= (4/3) × 3.14 × 1.0 × 10^(-13 × 3)
= (4/3) × 3.14 × 1.0 × 10^(-39)
= (4/3) × 3.14 × 1.0 × 10^(-39)
= 4.19 × 10^(-39) cm^3
Now, let's calculate the density of the proton using the formula:
Density (ρ) = Mass (m) / Volume (V)
Density = 1.7 × 10^(-24) g / 4.19 × 10^(-39) cm^3
We need to convert the volume to g/cm^3 by multiplying by 1 g/cm^3 = 1×10^3 g/cm^3:
Density = 1.7 × 10^(-24) g / (4.19 × 10^(-39) cm^3 × 1×10^3 g/cm^3)
Simplifying the units:
Density = (1.7 / 4.19) × 10^(-24-(-39+3)) g/cm^3
Density ≈ (1.7 / 4.19) × 10^(-24+36) g/cm^3
Density ≈ 0.406 × 10^12 g/cm^3
Change scientific notation to standard form:
Density ≈ 4.06 × 10^11 g/cm^3
Therefore, the density of a proton is approximately 4.06 × 10^11 g/cm^3.
You made a typo. Volume sphere = (4/3)*pi*r^3
Using the volume, calculate the volume of the sphere, then density = mass/volume
Post your work if you get stuck.