Question

Question #64a98

Answer 1

I get a value of the order of `10^14` for Hydrogen
and a value of the order of `10^13` for Uranium`"^238`

Explanation:

A. Let us take the example of hydrogen atom.
Atomic radius, Bohr's radius `a_0`: `5.29xx10^-11 m`
Atomic mass: `1.00794 u`
Nuclear diameter: `1.75×10^-15 m`
Mass of a proton: `1.00728u`

Average atomic density `rho_a="mass"/"volume"`
`=>rho_a=1.00794/(4/3pi(5.29xx10^-11)^3)`
Similarly Nuclear density `rho_n=1.00728/(4/3pi(1.75/2×10^-15)^3)`
Ratio of two densities `rho_n/rho_a=1.00728/1.00794xx((5.29xx10^-11)^3)/((0.875×10^-15)^3)`
`rho_n/rho_a`~`10^14`
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
B. Let us now take the example of Uranium`"^238` atom.
Atomic radius, empirical: `1.56 xx10^-10 m`
Average Atomic mass: `238.029 u`
Nuclear diameter: `15×10^-15 m`
Mass of nucleas: `238.0508u`

Average atomic density `rho_a="mass"/"volume"`
`=>rho_a=238.029/(4/3pi(1.56 xx10^-10)^3)`
Similarly Nuclear density `rho_n=238.0508/(4/3pi(15/2×10^-15)^3)`
Ratio of two densities `rho_n/rho_a=238.0508/238.029xx((1.56 xx10^-10)^3)/((7.5×10^-15)^3)`
`rho_n/rho_a`~`10^13`