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. (c) What is the mass of one 6.5-nm CdSe quantum dot?

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Convert the diameter of the quantum dot from nanometers to centimeters. Since 1 nm = 1 x 10^{-7} cm, multiply 6.5 nm by 1 x 10^{-7} to get the diameter in cm.

Calculate the volume of the quantum dot assuming it is spherical. Use the formula for the volume of a sphere: V = \frac{4}{3} \pi r^3, where r is the radius of the sphere. Remember to divide the diameter by 2 to get the radius.

Substitute the radius in centimeters into the volume formula to find the volume of the quantum dot in cm^3.

Use the density of CdSe to find the mass. The formula for mass is mass = density \times volume. Substitute the density (5.82 g/cm^3) and the calculated volume into this formula.

Calculate the mass of the quantum dot using the values obtained from the previous steps.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 Calculation

Density is defined as mass per unit volume and is a critical property for calculating the mass of an object when its volume is known. For a quantum dot, the volume can be calculated using its size (diameter) and the formula for the volume of a sphere. Once the volume is determined, the mass can be found by multiplying the volume by the density of the material.

Nanotechnology in Electronics

Nanotechnology involves manipulating matter at the atomic or molecular scale, typically between 1 and 100 nanometers. In electronics, materials like quantum dots are utilized to enhance performance, such as improving color accuracy and energy efficiency in displays. Understanding the implications of size and material properties is essential for leveraging nanotechnology in practical applications.

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Textbook Question

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?

Textbook Question

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?

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