CdSe quantum dots that are 6.5 nm in diameter emit red light upon stimulation. Assuming that the dot is a perfect sphere, calculate how many Cd atoms are in one quantum dot of this size.

Verified step by step guidance

First, calculate the volume of the quantum dot, assuming it is a perfect sphere. Use the formula for the volume of a sphere: \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere. Since the diameter is given as 6.5 nm, the radius \( r \) is half of that.

Convert the radius from nanometers to centimeters for consistency with typical density units. Remember that 1 nm = 1 x 10^-7 cm.

Next, determine the density of CdSe. You may need to look up the density of bulk CdSe, which is typically around 5.82 g/cm³.

Calculate the mass of the quantum dot using the formula: \( \text{mass} = \text{density} \times \text{volume} \).

Finally, calculate the number of Cd atoms in the quantum dot. First, find the molar mass of CdSe by adding the atomic masses of Cd and Se. Then, use Avogadro's number (6.022 x 10^23 atoms/mol) to convert the mass of the quantum dot to the number of moles, and subsequently to the number of Cd atoms, considering the stoichiometry of CdSe (1:1 ratio of Cd to Se).

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 quantum mechanical properties. Their electronic characteristics are closely related to their size, which allows them to emit specific colors of light when excited. The size of the quantum dot determines the energy levels of the electrons, influencing the wavelength of light emitted, such as the red light emitted by the CdSe quantum dots.

Volume of a Sphere

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius. This formula is essential for determining the total space occupied by the quantum dot, which is necessary for calculating the number of atoms it contains. Understanding how to apply this formula allows for the conversion of the dot's physical dimensions into a quantifiable volume.

Molar Mass and Density

Molar mass is the mass of one mole of a substance, while density is the mass per unit volume. For calculating the number of atoms in a quantum dot, knowing the molar mass of cadmium (Cd) and the density of CdSe is crucial. By using these values along with the volume of the quantum dot, one can determine how many cadmium atoms are present within it.

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Molar Mass Concept

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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?

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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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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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