# Problem: Very small crystals composed of 1000 to 100,000 atoms, called quantum dots, are being investigated for use in electronic devices.  (a) A quantum dot was made of solid silicon in the shape of a sphere, with a diameter of 9 nm . Calculate the mass of the quantum dot, using the density of silicon (2.3 g/cm3 ).

###### FREE Expert Solution

Recall that density is the ratio of the mass and volume of an object:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a sphere is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{4}}{\mathbf{3}}{{\mathbf{\pi r}}}^{{\mathbf{3}}}}$

where:

r = radius. Recall that diameter = 2r.

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###### Problem Details

Very small crystals composed of 1000 to 100,000 atoms, called quantum dots, are being investigated for use in electronic devices.  (a) A quantum dot was made of solid silicon in the shape of a sphere, with a diameter of 9 nm . Calculate the mass of the quantum dot, using the density of silicon (2.3 g/cm3 ).