phy2403 ps1 problem 2(d).  Phonon energy density.
Ratio of the phonon energy density to the rest-mass energy density (in hardwood).

cHardWood = Quantity[3960, "m/s"] ;(* https://www.engineeringtoolbox.com/sound-speed-solids-d_713.html *)
a0 = WolframAlpha["bohr radius in SI units",{{"Result",3},"QuantityData"}];
hbar = WolframAlpha["reduced Planck constant SI units",{{"Result",1},"QuantityData"}];
densityOfOak = WolframAlpha["convert oak wood density to SI units",{{"AdditionalConversion",1},"QuantityData"}];
cLight = WolframAlpha["convert speed of light to m/s",{{"Result",1},"QuantityData"}];

rho[k_,c_] := (1/(16 Pi^2)) hbar c k^4;
energyDensityPhonon = rho[1/a0, cHardWood];
oakRestMassEnergyDensity = UnitConvert[densityOfOak * cLight^2, "Joules/meter^3"];

{{"c", "=",cLight},{"(Subscript[c, hardwood])", "=",cHardWood},
{"(Subscript[a, 0])", "=",a0},{"ℏ", "=",hbar},
{"ρ-(Subscript[mass, oak])", "=",densityOfOak},
{"ρ-(Subscript[energy, phonon])", "=",energyDensityPhonon},
{"ρ-(Subscript[mass, oak]) (c^2)", "=",oakRestMassEnergyDensity},
{"ρ-(Subscript[energy, phonon])/(ρ-(Subscript[mass, oak]) (c^2))", "=",
energyDensityPhonon/oakRestMassEnergyDensity}} // Grid