Calculate the mass in grams of a these?

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 1.200 104 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.



help: aggradro's (sp?) number is 6.022 x 10^23

Answer 1

a) Silicium has an atomic mass of 28.0855 meaning that 6x10^23 atoms weight just that in grams. Therefore 1.2 x 10^4 atoms weigh 5.6x10^-19 grams
b) Divide the mass by the density to get the volume 2.4x10^-19 cm^3
c) This is the cubic root of the volume, hence 6.24x10^-7 cm

Answer 2

To find the mass of a quantum dot consisting of 1.200 104 atoms of silicon, you need to first find the number of moles, n, using Avogadro's number:

n = 1.200 104 / 6.022 x 10^23 = 1.992866 x 10^-18

now to find the mass, use the formula:

n = m/AM

where
m = mass (g)
AM = atomic mas (28.0855 gmol^-1 for Si)

so
m = n x AM
m = 1.992866 x 10^-18 x 28.0855

b) Having found the mass, you can find the volume if the density is known, using:

d = m/V

where
d = density (g/cm3)
m = mass (g)
V = volume (cm3)

c) For a cube, V = s^3, so take cube root of above.

I hope this helps.