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. (b) CdSe quantum dots that are 2.5 nm in diameter emit blue light upon stimulation. Assuming that the dot is a perfect sphere and that the empty space in the dot can be neglected, calculate how many Cd atoms are in one quantum dot of this size.

Verified step by step guidance

1. Calculate the volume of the quantum dot using the formula for the volume of a sphere: $V = \frac{4}{3} \pi r^3$, where $r$ is the radius of the sphere. Convert the diameter from nanometers to centimeters first.
2. Convert the volume from cubic centimeters to cubic meters if necessary, to match the units of density.
3. Use the density of CdSe (5.82 g/cm³) to find the mass of the quantum dot by multiplying the volume by the density.
4. Determine the molar mass of CdSe by adding the atomic masses of Cd and Se from the periodic table.
5. Calculate the number of moles of CdSe in the quantum dot by dividing the mass of the quantum dot by the molar mass of CdSe, and then use Avogadro's number to find the number of Cd atoms in the quantum dot.

Key Concepts

Quantum Dots

Quantum dots are nanoscale semiconductor particles that have unique optical and electronic properties due to quantum mechanics. Their size, typically ranging from 1 to 10 nanometers, allows them to emit light in specific colors when excited, which is a result of quantum confinement effects. The emission wavelength depends on the size of the dot, making them useful in applications like displays and biological imaging.

Volume and Density Calculations

To determine the number of atoms in a quantum dot, one must calculate its volume using the formula for the volume of a sphere (V = 4/3 π r³) and then use the density of the material to find its mass (mass = density × volume). This mass can then be converted to moles using the molar mass of the substance, allowing for the calculation of the number of atoms present in the quantum dot.

Atomic Composition and Molar Mass

The atomic composition of a compound, such as CdSe, is crucial for determining the number of atoms in a given mass. Each element has a specific molar mass, which is the mass of one mole of that element. For CdSe, the molar mass can be calculated by adding the molar masses of cadmium (Cd) and selenium (Se), enabling the conversion from moles to the actual number of atoms using Avogadro's number.