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:

$\boxed{\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a sphere is given by:

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

where: 

r = radius. Recall that diameter = 2r.