Brus equation emission energy Δ"E" = "hc"/λ, where c is the speed of light). This is useful for calculating the radius of a quantum dot from experimentally determined parameters. The overall equation is "E", "m"*, and "m"* are unique for each nanocrystal composition. For example, with CdSe nanocrystals: Brus equation The Brus equation can be used to describe the emission energy of quantum dot semiconductor nanocrystals (such as CdSe nanocrystals) in terms of the band gap energy "E", Planck's constant "h", the radius of the quantum dot "r", as well as the effective mass of the excited electron "m"* and of the
Kepler's equation distance from the centre of attraction along the ray. This equation is derived by multiplying Kepler's equation by 1/2 and setting "e" to 1: and then making the substitution Calculating "M" for a given value of "E" is straightforward. However, solving for "E" when "M" is given can be considerably more challenging. There is no closed-form solution. One can write an infinite series expression for the solution to Kepler's equation using Lagrange inversion, but the series does not converge for all combinations of "e" and "M" (see below). Confusion over the solvability of Kepler's equation has persisted in the literature