If the atom is assumed to be a sphere what is the volume in cm^3 of a single Au atom. Express answer using three significant figures

Answer 1

Kristy,

Great answer! However, there is one minor mistake in the Volume equation. V= 4/3π r³ not V= 3/4π r³

Best,

Paul.

Answer 2

Start with the formula for volume of a sphere:

V = 0.75*pi*(r^3)

You are looking for volume and you know what pi is, so you just need the radius of a single gold (Au) atom. If this is not given in your problem then you need to look up this value either in your textbook or online. There are many ways to calculate the radius and the most common way is to find the length of the Au-Au bond and divide that value in two. The atomic radius from my chemistry textbook is listed at 144 picometers or 144 pm.

Now just replace the "r" in the problem with 144 pm to solve for the volume.

V = 0.75*pi*(144^3)

V = 0.75*3.141592...*2985984 pm³

V = 7035559.049 pm³

Now we have an answer, but we are not done yet. The answer is not in cm³ and it is not in scientific notation.

V = 7.035559x10⁶ pm³

Now that we have scientific notation we can begin to change the answer to centimeters. 1 meter has 1x10¹² picometers and 1 meter also has 100 cm. Use these conversions to change the answer from picometers to centimeters. Remember that when changing for units in a power that the entire conversion must be raised to that power.

V = 7.035559x10⁶ pm³ x (1 m / 1x10¹² pm)³ x (100 cm / 1 m)³ =

I find it helpful to do the exponent math inside the conversions before calculating my final answer to avoid math mistakes.

V = 7.035559x10⁶ pm³ x (1 m³ / 1x10³⁶ pm³) x (1x10⁶ cm³ / 1 m³) =

V = 7.035559x10^-24 cm³

V = 7.04x10^-24 cm³ Final answer to three significant figures, rounding the last digit due to the "5" before the third significant figure.