Question #64a98

1 Answer
Mar 26, 2017

Answer:

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#