Problem: Very small semiconductor crystals composed of approximately 1000 to 100,000 atoms, are called quantum dots. Quantum dots made of the semiconductor CdSe are now being used in electronic reader and tablet displays because they emit light efficiently and in multiple colors depending on dot size. The density of CdSe is 5.82 g/cm3.CdSe quantum dots that are 6.5 nm in diameter emit red light upon stimulation. Assuming that the dot is a perfect sphere, calculate how many Cd atoms are in one quantum dot of this size.

FREE Expert Solution

Assuming 1 dot is a perfect sphere:

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

• Calculate the volume of a 6.5-nm dot

d = 6.5 nm
r = d/2 = 6.5/2 = 3.25 nm → convert to cm

$\mathbf{r}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{25}\mathbf{ }\cancel{\mathbf{nm}}\mathbf{\times }\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{ }\cancel{\mathbf{m}}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{nm}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{cm}}{{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\cancel{\mathbf{m}}}$

r = 3.25x10^-7 cm

$\mathbf{V}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}\mathbf{\pi }{\mathbf{(}\mathbf{3}\mathbf{.}\mathbf{25}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathbf{ }\mathbf{cm}\mathbf{)}}^{\mathbf{3}}$

V = 1.4379x10^-19 cm³

Calculate the mass of a 2.5 nm dot

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