Very small crystals composed of 1000 to 100,000 atoms, called quantum dots, are being investigated for use in electronic devices.
(a) Calculate the mass in grams of a quantum dot consisting of 1.400 104 atoms of silicon.
(b) Assuming that the silicon in the dot has a density of 2.3 g/cm3, calculate its volume.
(c) Assuming that the dot has the shape of a cube, calculate the length of each edge of the cube.
How many moles Si in the dot?
1.400 x 10^4 atoms/6.022 x 10^23 = ??moles.
Convert that to grams.
?? moles x molar mass Si = grams.
#2. mass = volume x density.
You have mass and density, calculate volume.
3. volume = length^3; calculate length.
Post your work if you get stuck.
To calculate the mass of a quantum dot consisting of 1.400 x 10^4 atoms of silicon, we need to know the molar mass of silicon.
(a) The molar mass of silicon is approximately 28.0855 g/mol. We can express this as:
Molar mass of silicon (Si) = 28.0855 g/mol
To find the mass of 1.400 x 10^4 atoms, we can use the equation:
Mass = (Number of atoms / Avogadro's number) x Molar mass
Given that the number of atoms is 1.400 x 10^4, and Avogadro's number is 6.022 x 10^23 atoms/mol, we can calculate the mass:
Mass = (1.400 x 10^4 / 6.022 x 10^23) x 28.0855 g/mol
Mass = 7.143 x 10^-19 g
Therefore, the mass of the quantum dot consisting of 1.400 x 10^4 atoms of silicon is approximately 7.143 x 10^-19 grams.
(b) To calculate the volume of the dot, we can use the equation:
Volume = Mass / Density
Given that the density of silicon is 2.3 g/cm^3, and the mass of the dot is 7.143 x 10^-19 g, we can calculate the volume:
Volume = 7.143 x 10^-19 g / 2.3 g/cm^3
Volume = 3.105 x 10^-19 cm^3
Therefore, the volume of the quantum dot is approximately 3.105 x 10^-19 cm^3.
(c) Assuming the dot has the shape of a cube, and knowing that the volume of a cube is given by:
Volume = Side length^3
We can rearrange the equation to solve for the side length:
Side length = Volume^(1/3)
Substituting the value of the volume we calculated in part (b), we can find the side length:
Side length = (3.105 x 10^-19 cm^3)^(1/3)
Side length = 1.478 x 10^-6 cm
Therefore, the length of each edge of the cube is approximately 1.478 x 10^-6 cm.
To calculate the mass of a quantum dot consisting of a certain number of atoms, we need to know the molar mass of the element. The molar mass of silicon (Si) is 28.09 g/mol.
(a) To calculate the mass in grams of a quantum dot consisting of 1.400 × 10^4 atoms of silicon, we can use the following formula:
mass = (number of atoms × molar mass) / Avogadro's number
Given:
Number of atoms of silicon (n) = 1.400 × 10^4 atoms
Molar mass of silicon (M) = 28.09 g/mol
Avogadro's number (NA) = 6.022 × 10^23 atoms/mol
Using the formula:
mass = (n × M) / NA
mass = (1.400 × 10^4 × 28.09) / (6.022 × 10^23)
mass ≈ 6.53 × 10^-19 grams
Therefore, the mass of the quantum dot consisting of 1.400 × 10^4 atoms of silicon is approximately 6.53 × 10^-19 grams.
(b) To calculate the volume of the dot, we can use the density formula:
density = mass / volume
Given:
Density of silicon (ρ) = 2.3 g/cm^3
Mass of the dot (m) = 6.53 × 10^-19 grams
Using the formula:
volume = mass / density
volume = (6.53 × 10^-19) / 2.3
volume ≈ 2.84 × 10^-19 cm^3
Therefore, the volume of the quantum dot is approximately 2.84 × 10^-19 cm^3.
(c) Assuming the dot has the shape of a cube, the length of each edge can be found by taking the cube root of the volume:
edge length = (volume)^(1/3)
edge length = (2.84 × 10^-19)^(1/3)
edge length ≈ 6.69 × 10^-7 cm
Therefore, the length of each edge of the cube-shaped quantum dot is approximately 6.69 × 10^-7 cm.