Answer :
Answer:
δ = 3.962 E14 g/cm³
Explanation:
- δ ≡ mass / volume [=] g/cm³
∴ mass proton = 1.0073 amu
∴ amu ≡ 1.66054 E-24 g
⇒ g proton = (1.0073 amu)×(1.06654 E-24 g/amu) = 1.074 E-24 g
- V = 4/3πr³
∴ r = D/2 = (1.73 E-15 m)/2 = 8.65 E-16 m
⇒ V = (4/3)π(8.65 E-16 m)³
⇒ V = (2.711 E-45 m³)×(1000000 cm³/m³) = 2.711 E-39 cm³
⇒ δ = (1.074 E-24 g)/(2.711 E-39 cm³)
⇒ δ = 3.962 E14 g/cm³
Answer:
Density = 6.17 * 10^14 g/cm³
Explanation:
Given Parameters
Mass of the proton = 1.0073 amu
Diameter of the proton = 1.75 * 10^-15 m
Required:
Calculate the density of the proton.
Density is calculated using the following formula;
Density = mass / volume
Where mass should be in grams and volume should be in cm ³
Calculating mass of a proton in grams.
Mass = 1.0073 amu
First, we convert to kilogram
Mass = 1.0073 * 1.66054 * 10^-27 kg
Then we convert to grams
Mass = 1.0073 * 1.66054 * 10^-27 * 10³ g
Mass = 1.0073 * 1.66054 * 10^-24 g
Mass = 1.673 * 10^-24 g
Then we calculate the volume of the proton
Volume = 4/3πR³ where R = Radius
And R = ½d.
First calculate the radius in centimetres
R = ½ * 1.73 * 10^-15 m
R = 0.865 * 10^-15
Convert to centimetres
R = 0.865 * 10^-15 * 10² m
R = 0.865 * 10^-13 cm
So, Volume = 4/3 * 3.14 * (0.865 * 10^-13)³
Volume = 4.187 * (0.865 * 10^-13)³
V = 4.187 * 0.865³ * 10^-39
V = 2.71 * 10^-39cm³
So, density = Mass / Volume becomes
Density = 1.673 * 10^-24 g / 2.71 * 10^-39cm³
Density = 0.617 * 10^15 g/cm³
Density = 6.17 * 10^14 g/cm³