Question

The spec sheets for Lumidot quantum dots from Sigma-Aldrich scientific supply company specifies the following core sizes (radius of the quantum dots) and wavelengths for their various dots:

Radius (nm) wavelength(nm)

3.0 510

3.3 530

3.4 560

4.0 590

5.2 610

6.3 640

Use this data to verify that the 1/R² dependence of E_ph = E_g + n (h²/(8m_eR²) and to find the band gap energy (Hint: calculate E_ph for each of these wavelengths, the plot E_ph versus 1/R² )

Answer 1

A(X1) B(Y1) C(X2) D(Y2) radius (nm) wavelength(nm) /R 2 Energy-1240/wavelength 510 530 560 590 610 640 2.43137 2.33962 2.21429 2.10169 2.03279 1.9375 3.3 4 5.2 6.3 0.09183 0.08651 0.0625 0.03698 0.0252

Energy=1240/wave length Linear Fit D 2.5 Equation Weight Residual Sum of Squares Pearsons r Adj. R-Square No Weighting 0.00795 0.9772 0.94385 Value Standard Error Intercept Slope 1.79727 5.49033 0.04501 0.59645 2.3 o 2.2 2.0 0.02 0.04 0.06 0.08 0.10 0.12 1/RA2

Energy is calculated from the relation E=hc/(wavelength), where hc=1240nm.eV and wavelength is in nm.

From the graph, it is clear that Energy(Eph) is varying approximately linearly with 1/R² .

And from the straight equation y=mx+c we can find out the value of c which is y-intercept and from here c is the band gap Eg. And from the above data Eg is 1.797eV.