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?

Verified step by step guidance

1. Calculate the volume of a single 2.5-nm quantum dot using the formula for the volume of a sphere: $V = \frac{4}{3} \pi r^3$, where $r$ is the radius in centimeters.
2. Calculate the volume of a single 6.5-nm quantum dot using the same formula for the volume of a sphere.
3. Determine the number of 2.5-nm dots needed to make one 6.5-nm dot by dividing the volume of the 6.5-nm dot by the volume of a 2.5-nm dot.
4. Calculate the total number of CdSe formula units in the 6.5-nm dot using the density of CdSe and the volume of the 6.5-nm dot.
5. Determine how many CdSe formula units would be left over by subtracting the number of formula units used in the 2.5-nm dots from the total number of formula units in the 6.5-nm dot.

Key Concepts

Quantum Dots

Quantum dots are nanoscale semiconductor particles that have unique optical and electronic properties due to their size. Their ability to emit light in various colors is size-dependent, meaning that smaller dots emit different wavelengths than larger ones. This property makes them valuable in applications like displays and sensors.

Volume and Density Calculations

To determine how many smaller quantum dots are needed to create a larger one, one must understand the relationship between volume and density. The volume of a dot can be calculated using its radius, and the density allows for the conversion between mass and volume. This is essential for calculating how many smaller dots fit into the volume of the larger dot.

Molar Mass and Formula Units

The molar mass of a substance, such as CdSe, is crucial for converting between grams and moles, which helps in determining the number of formula units in a given mass. Understanding how to calculate the number of formula units from the mass of the material allows for accurate assessments of leftover material after forming larger structures from smaller ones.