Very small semiconductor crystals, composed of approximately 1000 to 10,000 atoms, are called quantum dots. Quantum dots made of the semiconductor CdSe are now being used in electronic reader and tablet displays because they emit light efficiently and in multiple colors, depending on dot size. The density of CdSe is 5.82 g/cm3. (e) If you wanted to make one 6.5-nm dot from multiple 2.5-nm dots, how many 2.5-nm dots would you need, and how many CdSe formula units would be left over, if any?

Video transcript

Hi everyone here we have a question asking us how many? 6.7 nanometer Silicon quantum dots are needed to create 1, 12 nanometer dot. If the density of silicon is 2.33 g per milliliters, how many formula units of silicon are left over? So we are going to use the volume of the sphere Which is 4/ times pi times our radius cubed. So we are going to go from diameter two radius to volume. So step one is going to be to calculate the volume of silicon dots. So the diameter is 6.7 nm Which means that the radius is 6.7 divided by two Which equals 3. nm. So the volume equals 4/ times pi Times 3. nm cubed Which equals 157. nm cubed. And that is the volume of silicon dots. So our step two is going to b to calculate the volume of silicon dots as well. So we can find how many dots are needed to make nm. So our diameter for this one is nm. So our radius is going to equal 12 divided by two which equals six nanometers. So our volume equals 4/ times pi times six nanometers squared And that equals 904. nm cubed silicon dots. So our step three is to calculate the number of 6. nanometer dots needed to make a 12 nanometer dot. So we have 904. nm cubed Divided by .4791 nmeter cubed Equals 5.7454 silicon dots. So we're going to round that to six, 6.7 nanometer dots. And for step four we're going to calculate our leftover 6.7 nanometer dots. So we have six -5. which equals 0.2546. Now we're going to go from volume to mass two moles to formula units. So we have 57. 91 nm Cube. And that is our area Times one times 10 To the negative, 21st cm cubed over one nanometer cubed, Times one mil liter over one centimeter cubed Times 2.33g of silicon over one mill leader times one mole Over silicon Mueller mass, which is 28.09 g times avocados number. So 6.22 times 10 to the 23rd formula units over one mold. So are nanometers cubed, are going to cancel out our centimeters cubed are going to cancel out our milliliters are going to cancel out our grams of silicon are going to cancel out our moles are going to cancel out giving us 7866. formula units. Next we have 0. 46 dots Times our 7866. Formula units over one dot And our dots cancel out. And that gives us 2003 formula units. And where you're going to put that into scientific notation. So we're going to Take our decimal point to the left, 123 spots, so 2.0 times To the 3rd Formula Units. And that is our final answer. Thank you for watching. Bye.