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. (a) What is the mass of one 2.5-nm CdSe quantum dot?

검증된 단계별 안내

Determine 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 quantum dot. Convert the diameter from nanometers to centimeters first.

Calculate the radius of the quantum dot by dividing the diameter by 2.

Substitute the radius into the volume formula to find the volume in cubic centimeters.

Use the density formula \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\) to solve for the mass. Rearrange the formula to \(\text{Mass} = \text{Density} \times \text{Volume}\).

Substitute the given density of CdSe and the calculated volume into the mass formula to find the mass of the quantum dot.

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Quantum Dots

Quantum dots are nanoscale semiconductor particles that have unique optical and electronic properties due to their size. They can emit light in various colors when excited, which is a result of quantum confinement effects. The size of the quantum dot determines the wavelength of light emitted, making them useful in applications like displays and biological imaging.

Density and Volume Calculations

Density is defined as mass per unit volume and is a critical concept in determining the mass of an object when its volume is known. For a quantum dot, the volume can be calculated using the formula for the volume of a sphere (V = 4/3 π r³), where r is the radius. By knowing the density of CdSe, one can find the mass by rearranging the density formula (mass = density × volume).

Nanotechnology and Scale

Nanotechnology involves manipulating matter at the atomic or molecular scale, typically between 1 and 100 nanometers. At this scale, materials can exhibit different physical and chemical properties compared to their bulk counterparts. Understanding the implications of size on properties is essential for applications in electronics, medicine, and materials science, particularly for substances like quantum dots.