The atomic radius of Pb is 175 pm, and the density is 11.34 g>cm3. Does lead have a primitive cubic structure or a face-centered cubic structure?

Video transcript

Hey everyone, we're told that platinum has an atomic radius of 139 PICO meters and a density of 21.4 g per cubic centimeter. What type of structure will platinum have? Looking at our answer choices, Let's think about what we've learned. We know that if it is a primitive cubic structure or a simple cubic, this will have one atom per unit cell in comparison to a body centered structure. This will have two atoms per unit cell. Now looking at a face centered cubic structure, this will have four atoms per unit cell. Now let's first calculate the volume of our unit cell and we can do so by taking our edge length which is symbolized by A And this is going to be equal to two times the square root of two times our radius plugging in our values we get two times the square root of two times our radius of 139 PICO meters. This will get us to an edge length of 393.1514 km. But since we do want this in cm, let's go ahead and use our dimensional analysis to convert this. So we know that one PICO meter contains 10 to the negative m. And we also know that one cm contains 10 to the negative two m. Now when we calculate this out and cancel out our units, we end up with an edge length of 3. times 10 to the negative eight centimeters. Now let's go ahead and calculate our volume and we can do so by taking our edge link and cubing it. So plugging in our edge length of 3.931514 times 10 to the negative eight cm we can go ahead and cube this value. And when we do so we end up with a volume of 6.0769 times 10 to the negative 23 cc. Now that we have our volume. Let's go ahead and determine the number of atoms we have per unit cell. Starting with our volume, we have 6.769 times 10 to the negative 23rd cubic centimeters per unit cell. Next using our dimensional analysis, We're going to take our density which they provided to us and we know that we have 21. g per one cc. Next taking platinum's molar mass, we know that we have 195. g of platinum per one mole a platinum. And lastly using avocados number, We know that we have 6.022 times 10 to the 23rd atoms per mole. And when we calculate this out and cancel out all of our units, we end up with a value Of 4.01. Which we can round to four atoms per unit cell. Now going back to our answer choices, it looks like our answer here is going to be c since we determined that we had four atoms per unit cell. Now, I hope that made sense and let us know if you have any questions.