Help me answer this! Best answer gets 10 points.?
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 1.500 104 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.
sorry i mean 1.500
i meant 1.05 104 Atoms two separate numbers
1.500 104 atoms
- 1 decade agoFavorite Answer
You just said the crystals consist of 1000 to 100,000 atoms
then you give a problem where the dot has
1,500,104 atoms of silicon, unless you meant to type 1,500
atoms. or 150,104 which is still larger than 100,000 .
I'm not sure whether or not you typed what you mean.
I just realized, you may have meant 1.500 times 10^4 which
is 15,000 and would fit the definition of a quantum dot that
Please use the ^ to indicate "to the power of" because
104 means ONE HUNDRED FOUR , not 10 to the fourth power.
First we note the atomic mass of silicon is 28.0855
That means that one mole of it weighs 28.0855 grams
A mole, however is 6.022 x 10^23 atoms
so the mass of this dot is
28.0855 grams/mole x [1 mole]/ [6.022 x10^23]atoms x [1.500 x 10^4]atoms/ 1
=6.99572 x 10^(-19) grams = 6.996 x 10^(-19) grams
to 4 significant figures
b) Since density = mass/volume
density times volume = mass and
volume = mass/density =6.996 x 10^(-19) grams/ 2.3 grams/cm^3
= 3.04162 x 10^(-19) cubic centimeterss
= 3.042 x 10^(-19) cc if we must round to 4 sig figs, 3 to right of decimal
c. The length of each edge of the cube would be the
cube root of the volume we just figured.
That is [3.04162 x 10^(-19)]^(1/3)
=6.725 x 10^(-7) cm = 6.725 x 10^(-9) meters
= 6.725 nanometers = 67.25 angstrom unitsSource(s): http://www.ktf-split.hr/periodni/en/ For a periodic table of elements
- Anonymous1 decade ago
The atomic mass of silicon is 28.0855, so 6.02x10²³ Si atoms weigh 28.0855g.
a) 28.0855g / 6.02x10²³ atoms x 1500104 atoms = 7.00x10^-17g
b) 7.00x10^-17g x 1 cm³ / 2.3g = 3.04x10^-17 cm³
c) (3.04x10^-17)^(1/3) = (30.4x10^-18)^(1/3) = 3.12x10^(-6) cm = 31.2 nmSource(s): Double-check my work Also, I'm not sure if you meant 1.5 million atoms, because of the way you typed it. If not, you'll have to adjust the results accordingly. It looks almost halfway European, but not even completely that, so I'm out of guesses. Especially since you say that the number is usually between a thousand and a hundred thousand.