Hi guys,

I am studying for a MChem Chemistry and have taken on some extra short courses to help with my learning. I am currently mid-way through my nanochemistry short course. Today we were asked to estimate the size of a nanoparticle using a simplified equation, and whilst I have an answer, I know it is too large by a magnitude of 10. I will post the question below:

*To synthesise cadmium sulfide CdS nanocrystals in aqueous solution, 1L of 2 mM solution of CdSO4⋅2.5H2O was mixed with 18 mmol of 1-thioglycerol under stirring (200 rpm, 5 min). Unknown amount of ammonium sulfide was rapidly added under ambient conditions. The resulting solution had room temperature photoluminescence centred at 460 nm. Transmission electron microscopy studies revealed the average size of the nanocrystals of 3.8 nm. **Estimate the size of the nanoparticles from their optical properties using the simplified equation below and compare it to the experimental value. Explain any differences observed. Include unit analysis. *

*EE(QD)=E*_{g}, + (ħ^{2}pi^{2} / 2m_{eh}R^{2})

I related the wavelength to energy and substituted that into the equation and have got an answer of 72 nm, which is obviously too large. I would really appreciate some help with this one if possible. Many thanks.

EDIT - m

_{eh} is the effective mass of the electron and hole

R is the radius of the atom