Barium has a density of 3.59 g/cm3 and crystallizes with the body-centered cubic unit cell. Calculate the radius of a barium atom.

Video transcript

Hey everyone in this example, we need to calculate the radius of a chromium atom Given that it has a body centered cubic unit cell and a density of 7. g per cubic centimeter. So what we want to recognize is our adam chromium on the periodic table. Cr And we would see that it has a molar mass equal to a value of 52.0 g per mole. We're going to use the smaller mass as a conversion factor to find the mass of the body centered cubic unit cell by taking the fact that for one unit cell we can Showcase two of our atoms because we want mass and grams. We're going to multiply by our molar mass as a conversion factor where we recognize that we have for one mole of our Adam Chromium, A molar mass of 52 from the periodic table, g of chromium. And then now we're going to multiply to get rid of that mole term, Buy avocados number. Where we recalled that for one mole we have six point oh 22 times 10 to the 23rd power atoms. So now we're able to cancel out moles as well as Adam's. Sorry. So Adams are right here and we're going to also be able to what will be left with grams per unit cell as our unit for mass, which is what we want for the mass of our cubic unit cell. And this is going to give us a mass equal to 1.73 times 10 to the negative 22nd power grams per unit cell. So we're given density in our prompt as this value circled. And what we want to do is get our volume By taking our mass and dividing it by our density value. And so we found our mass of our cubic unit cell above as 1.73 times 10 to the negative 22nd power g per unit cell. And this is going to be divided by our density from the prompt as 7. grams per cubic centimeter. And so what we're going to be able to do is get rid of our units of grams. And so we're going to get a volume equal to a value of 2.40 times 10 to the negative 23rd power cubic centimeters per unit cell. So now we want to find the length of our cubic unit cell and we should recall that to find length. We would take the cube root of our volume. And so what we would get is the cube root Of our volume which we found above as 2.40 Times 10 to the negative 23rd power cubic centimeters. And so this gives us a value equal to 2. times 10 To the negative 8th power. And we're left with these units of centimeters. However, we want our length to be in units of meters. So we're going to convert from centimeters to PICO meters by recalling that our prefect senti tells us we have 10 to the 10th power PICO meters. So now we're able to cancel centimeters we're left with PICO meters. And what we should get for length is that length is equal to a value Of 2 88. m. So now that we have the length of our cubic unit cell, the prompt wants us to find radius and we would take our radius And recall to our formula where length is equal to four times the radius divided by three to the point fifth power. So we would reorganize this to sulfur radius so that we have radius is equal to three to the point fifth power multiplied by a value for length. So what this should give us is three to the point fifth power multiplied by our length which above we found us to 88.45 m. And so what this is going to give us Is a value of 499.61. And we just need to divide by four so that we get our final radius as a value equal to and I'll just move everything over to the right actually so that we have enough room. So what we're going to get for radius after we divide by four is a value of 124.9 PICO meters. And we can round this to a value of about 125 km as our final answer. So what's highlighted in yellow is our final answer for the radius of our atom of chromium. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.