Question #64a98

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Question #64a98

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Answer 1 · 2017-03-26T08:25:19

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

Explanation:

A. Let us take the example of hydrogen atom.
Atomic radius, Bohr's radius $a_{0}$ $a_0$ : $5.29 \times 10^{- 11} m$ $5.29xx10^-11 m$
Atomic mass: $1.00794 u$ $1.00794 u$
Nuclear diameter: $1.75 \times 10^{- 15} m$ $1.75×10^-15 m$
Mass of a proton: $1.00728 u$ $1.00728u$

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

Average atomic density $ρ_{a} = \frac{mass}{volume}$ $rho_a="mass"/"volume"$
$\Rightarrow ρ_{a} = \frac{238.029}{\frac{4}{3} π {(1.56 \times 10^{- 10})}^{3}}$ $=>rho_a=238.029/(4/3pi(1.56 xx10^-10)^3)$
Similarly Nuclear density $ρ_{n} = \frac{238.0508}{\frac{4}{3} π {(\frac{15}{2} \times 10^{- 15})}^{3}}$ $rho_n=238.0508/(4/3pi(15/2×10^-15)^3)$
Ratio of two densities $\frac{ρ_{n}}{ρ_{a}} = \frac{238.0508}{238.029} \times \frac{{(1.56 \times 10^{- 10})}^{3}}{{(7.5 \times 10^{- 15})}^{3}}$ $rho_n/rho_a=238.0508/238.029xx((1.56 xx10^-10)^3)/((7.5×10^-15)^3)$
$\frac{ρ_{n}}{ρ_{a}}$ $rho_n/rho_a$ ~ $10^{13}$ $10^13$

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Question #64a98

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