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What is the best answer for the radius of a spherical atom?

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By definition, density is mass divided by volume, `D = m/V` , so if we are given the mass and density, we can solve for the volume by `V = m/D` .

The density is `1.0*10^14 g/cm^3` and the mass is `2.0*10^-23 g` .

`V = m/D = (2.0*10^-23 g)/(1.0*10^14 g/cm^3) = 2.0*10^-37 cm^3`

We're told to assume the atom is spherical, so we can get the radius by using the volume formula for a sphere, `V = 4/3 pi r^3`, which we solve for r to get `r = (V/(4/3pi))^(1/3)`.

`r = ((2.0*10^-37 cm^3)/(4/3 pi))^(1/3) = (4.775*10^37 cm^3)^(1/3) = 3.628*10^-13 cm.`

The result is `3.6*10^-13 cm`, which is choice A.


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