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

`r=76pc`

Step-by-step explanation:

Hello,

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

`V=(4)/(3) \pi r^3`

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

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

Best regards.

Answer 2

Volume of sphere =
`(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* 10^(-30)m^(3)`)

Thus,

`1.9* 10^(-30)m^(3) = (4)/(3)\3.14 r^(3)`

`1.9* 10^(-30)m^(3) = 4.1867 r^(3)`

`r^(3) = (1.9* 10^(-30)m^(3))/(4.1867)`

`r^(3) = 0.453* 10^(-30)m^(3)`

`r = \sqrt[3]{0.453* 10^(-30)m^(3)}`

=
`0.768* 10^(-10)m`

=
`7.68* 10^(-12)m`

=
`7.68 picometers`

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