Respuesta :
Answer:
The fraction of the volume of the atom that is taken up by the nucleus is [tex]4.6656\times 10^{-14}[/tex].
The density of a proton is [tex]6.278\times 10^{14} g/cm^3[/tex].
Explanation:
Diameter of the atom ,d = 2.50 Å
Radius of the atom ,r = 0.5 d=0.5 × 2.50 Å = 1.25Å
Volume of the sphere= [tex]\frac{4}{3}\pi r^3[/tex]
Volume of atom = V
[tex]V=\frac{4}{3}\pi r^3[/tex]..[1]
Diameter of the nucleus ,d' = [tex]9.00\times 10^{-5}\AA[/tex]
Radius of the nucleus ,r' = 0.5 d'=[tex]0.5\times 9.00\times 10^{-5}\AA=4.5\times 10^{-5}\AA[/tex]
Volume of nucleus = V'
[tex]V=\frac{4}{3}\pi r'^3[/tex]..[2]
Dividing [2] by [1]
[tex]\frac{V'}{V}=\frac{\frac{4}{3}\pi r'^3}{\frac{4}{3}\pi r^3}[/tex]
[tex]=\frac{r'^3}{r^3}=\frac{(4.5\times 10^{-5}\AA)^3}{(1.25 \AA)^3}[/tex]
[tex]\frac{V'}{V}=4.6656\times 10^{-14}[/tex]
The fraction of the volume of the atom that is taken up by the nucleus is [tex]4.6656\times 10^{-14}[/tex].
Diameter of the proton ,d = [tex]1.72\times 10^{-15} m = 1.72\times 10^{-13} cm[/tex]
1 m = 100 cm
Radius of the proton,r = 0.5 d=[tex]0.5\times 1.72\times 10^{-13} cm=8.6\times 10^{-14} cm[/tex]
Volume of the sphere= [tex]\frac{4}{3}\pi r^3[/tex]
Volume of atom = V
[tex]V=\frac{4}{3}\times 3.14\times (8.6\times 10^{-14} cm)^3=2.664\times 10^{-39}cm^3[/tex]
Mass of proton, m = 1.0073 amu = [tex]1.0073\times 1.66054\times 10^{-24} g[/tex]
[tex]1 amu = 1.66054\times 10^{-24} g[/tex]
Density of the proton : d
[tex]d=\frac{m}{V}=\frac{1.0073\times 1.66054\times 10^{-24} g}{2.664\times 10^{-39}cm^3}=6.278\times 10^{14} g/cm^3[/tex]
The density of a proton is [tex]6.278\times 10^{14} g/cm^3[/tex].
