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Question

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.

Update:

sorry i mean 1.500

Update 2:

i meant 1.05 104 Atoms two separate numbers

Update 3:

1.500 104 atoms

Answer 1

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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

you supplied.

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 units

Source(s): http://www.ktf-split.hr/periodni/en/ For a periodic table of elements

Answer 2

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 nm

Source(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.