Volume of sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]
where, [tex]\pi[/tex] = [tex]3.14[/tex]
r = radius of sphere
Put the given value of volume in above formula i.e. ([tex]1.9\times 10^{-30}m^{3}[/tex])
Thus,
[tex]1.9\times 10^{-30}m^{3} = \frac{4}{3}\3.14 r^{3}[/tex]
[tex]1.9\times 10^{-30}m^{3} = 4.1867 r^{3}[/tex]
[tex]r^{3} = \frac{1.9\times 10^{-30}m^{3}}{4.1867}[/tex]
[tex]r^{3} = 0.453\times 10^{-30}m^{3}[/tex]
[tex]r = \sqrt[3]{0.453\times 10^{-30}m^{3}}[/tex]
= [tex]0.768\times 10^{-10}m[/tex]
= [tex]7.68\times 10^{-12}m[/tex]
= [tex]7.68 picometers[/tex]
Thus, radius of the carbon atom is [tex]7.68 picometers[/tex]
Answer:
[tex]r=76pc[/tex]
Explanation:
Hello,
In this case, we consider the volume of a sphere given by:
[tex]V=\frac{4}{3} \pi r^3[/tex]
Solving for the radius as we know the volume of the carbon atom we obtain:
[tex]r=\sqrt[3]{\frac{3V}{4\pi}} =\sqrt[3]{\frac{(3)(1.9x10^{-30}m^3)}{4\pi}} \\r=77x10^{-12}m*\frac{1pc}{1x10^{-12}m} \\\\r=76pc[/tex]
Best regards.
