Ond we need some way of quantitatively assessing the strength of a transition. What is the intensity of the electronic absorption? We do that with something called the Bealambat Law. We can use the Bealambat Law to assess the amount of light transmitted by our sample and then we can extract from that a constant, which will call the molar the catech absorption coefficient or the extinction coefficient, which characterises the strength of a transition. That will allow us to say more precisely what we mean by a weak transition or a strong transition. We are going to derive the Bealambat Law. There is our sample, which has got some light coming in from the left as you look at it. It is hitting our sample and then we have broken our sample up into lots of thin strips of length delta L. The light that is transmitted has intensity i- and the length of that is delta L. The amount of light transmitted is expressed as a fraction of the incident intensity. We do i1-i, transmitted intensity, minus the incident intensity, and then we divide it by the incident intensity. We call that delta i over i. That is the fraction of light transmitted by that thin strip of length delta L. In general, what is the intensity or the relative light transmitted going to depend upon? It is going to depend upon whether or not the photon bangs into a molecule as it goes through the sample. If it does not bang into a molecule, then it is not going to be absorbed. Therefore, our delta i over i depends on the concentration of the sample. Also, it depends on of course on delta L. If the sample is longer, then there is a greater chance that the photon of light will be absorbed because it has a greater chance of encountering an absorbing molecule. So delta i over i is going to be proportional to concentration and delta L, the length of that strip of the sample. We put a constant of proportionality in there, which I am calling kappa. Since the way we have defined delta i is always negative, then that is where the negative sign comes from. If we want to know the total transmission of our entire sample, then we just have to add together all of those individual elements. If we make delta L very small, we do not have to sum up all those individual elements. We can replace the summation sign by an integration sign. The delta i becomes very small. We call it di. We integrate di over i. We are now calling our intensity, which hits the zeroth strip, i0. We integrate over all of those strips until we get to the final intensity i. That gives you the equation l and i over i0 is equal to minus kCl. Which we can rewrite, of course, as an exponential function, i is equal to i0 to each of the minus kCl. The traditional way to assess logarithm of i over i0 is to use log to the base 10. We write that as log to the base 10. That means on the right hand side we have to make a correction, dividing by 2.303. We include that 2.303 correction into our constant of proportionality, which was k. Now it becomes epsilon. Epsilon is just k divided by 2.303. Epsilon is what we call the molar-dicatic absorption coefficient. It is a function of the molecule. It is independent of the concentration or the length of the sample. It tells us about the propensity of the molecule to absorb light. If epsilon is a large number, then that is a strong transition. If it is a small number, then it is a weak transition. If it is zero, but the energy levels are there, then it is a forbidden transition. So having this epsilon allows us to be quantitative about the strength of electronic transitions. That whole thing EpsilonCl is sometimes referred to as the absorbance. And that equation there, log to the base 10, i over i0 is equal to minus epsilonCl. It is known as the billand at law.