Question

The volume of a carbon atom is 1.9 x 10–30 m3. What is the radius of the atom in picometers? The volume of a sphere is (4/3)(pi)r3

Answer 1

Answer:

$r=76pc$

Explanation:

Hello,

In this case, we consider the volume of a sphere given by:

$V=\frac{4}{3} \pi r^3$

Solving for the radius as we know the volume of the carbon atom we obtain:

$r=\sqrt[3]{\frac{3V}{4\pi}} =\sqrt[3]{\frac{(3)(1.9x10^{-30}m^3)}{4\pi}} \\r=77x10^{-12}m*\frac{1pc}{1x10^{-12}m} \\\\r=76pc$

Best regards.

Answer 2

Volume of sphere = $\frac{4}{3}\pi r^{3}$

where, $\pi$ = $3.14$

r = radius of sphere

Put the given value of volume in above formula i.e. ($1.9\times 10^{-30}m^{3}$)

Thus,

$1.9\times 10^{-30}m^{3} = \frac{4}{3}\3.14 r^{3}$

$1.9\times 10^{-30}m^{3} = 4.1867 r^{3}$

$r^{3} = \frac{1.9\times 10^{-30}m^{3}}{4.1867}$

$r^{3} = 0.453\times 10^{-30}m^{3}$

$r = \sqrt[3]{0.453\times 10^{-30}m^{3}}$

= $0.768\times 10^{-10}m$

=  $7.68\times 10^{-12}m$

=  $7.68 picometers$

Thus, radius of the carbon atom is $7.68 picometers$