Question

Using the mass of a proton 1.0073 amu and assuming it's diameter is1.0x10^-15, calculate the density of a proton in g/cm^3. I'm not sure about how to convert amu to grams. Thanksfor the help!!

Answer 1

You just have to find a conversion from amu to grams. For every 1 amu, there is 1.66×10⁻²⁴ grams. Thus,

Mass of proton = 1.0073 amu * 1.66×10⁻²⁴ grams/amu = 1.672×10⁻²⁴ grams

Since a proton is spherical in shape, the volume would be:

Volume = 1/6*πd³ = 1/6*π(1.0×10⁻¹⁵ cm)³ = 5.236×10⁻⁴⁶ cm³

Therefore, the density is equal to

Density = Mass/Volume = 1.672×10⁻²⁴ grams/5.236×10⁻⁴⁶ cm³
Density = 3.2×10²¹ g/cm³