I believe you may have omitted the power of 10 for part A.
For part b I get 1.68 but not the 10^-8
My answers:
4.00 g/ cm^3
1.68 x 10^-8 kg
For part b I get 1.68 but not the 10^-8
(1.675*10^-24 g)/(4/3 π *10^-39 cm^3) = 4.00*10^14 g/cm^3
so, a .01cm ball would have a mass of
(4/3 π * 10^-6 cm^3)(4.00*10^14 g/cm^3) = 1.68*10^6 kg
You must have realized your values were kinda low. The whole point of the exercise was showing how incredibly dense neutron stars are.
Given:
Radius of a neutron (r) = 1.0 x 10^-13 cm
Volume of a sphere (V) = (4/3) * π * r^3
Let's begin by finding the volume of a neutron:
V = (4/3) * π * (1.0 x 10^-13)^3 cm^3
V ≈ 4.19 x 10^-39 cm^3
Next, we need to convert the density from g/cm^3 to kg/m^3.
1 g/cm^3 is equivalent to 1000 kg/m^3.
Density of a neutron (D) = 4.00 g/cm^3 * 1000 kg/m^3
D = 4000 kg/m^3
Now, we can proceed to find the mass of the pebble-sized piece of a neutron star.
Radius of the pebble (r) = 0.10 mm = 0.10 x 10^-2 cm
Volume of the pebble (V) = (4/3) * π * (0.10 x 10^-2)^3 cm^3
V ≈ 4.19 x 10^-9 cm^3
Mass of the pebble (M) = Density * Volume
M = 4000 kg/m^3 * (4.19 x 10^-9 cm^3 * 1 m^3 / 10^6 cm^3)
Converting cm^3 to m^3:
1 cm^3 = (1/10^6) m^3
M ≈ 4000 kg/m^3 * 4.19 x 10^-15 m^3
M ≈ 1.68 x 10^-11 kg
Therefore, the mass of a small piece of a neutron star the size of a spherical pebble is approximately 1.68 x 10^-11 kg.
Given that the radius of a neutron is approximately 1.0 x 10^-13 cm, we can substitute this value into the formula:
V = (4/3)Ï€(1.0 x 10^-13 cm)^3
Simplifying this expression, we get:
V ≈ (4/3)π(1.0 x 10^-13)^3 cm^3
Next, we can calculate the mass (in kg) of a small piece of a neutron star with the size of a spherical pebble, using the assumption that the neutron star has the same density as a neutron.
To do this, we need to know the density of a neutron in grams per cm^3. Converting the units, we have:
Density of a neutron = 4.00 g/cm^3
Now, let's calculate the mass of the pebble-sized piece of a neutron star:
1. Convert the radius of the pebble from 0.10 mm to cm:
The radius of the pebble = 0.10 mm = 0.10 x 10^-1 cm
2. Calculate the volume of the pebble:
V = (4/3)Ï€(0.10 x 10^-1 cm)^3
3. Multiply the volume by the density of a neutron:
Mass = V x Density of a neutron
By following these steps, we can find the mass of a small piece of a neutron star the size of a spherical pebble with a radius of 0.10 mm.
Calculating the mass, we get:
Mass ≈ 1.68 x 10^-8 kg