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I'm self-teaching calculus and I'm looking at exponential growth and decay. The differential equation for relationships like these if this was related to time is

dP/dt = -kP

i.e. the rate of change in P with time decreases at a rate which is proportional to the amount of P present. I can understand this equation if it relates to, say, the change in concentration of a reactant with time during a reaction.

I was then trying to apply the same understanding to the exponential decrease in transmission of light through a sample in a UV spectrometer as concentration increases

If i relate this to the picture I have attached, it looks as if to transmission of light drops 50% for a particular concentration of light absorbing molecules.

For a particular concentration of solution, 50% of the incident light is absorbed. If you then add this amount again, another 50% of the incident light is absorbed (which is 50% of the remaining 50% = 25%, leaving 25% light and 75% absorbed)

I can't really understand the chemical basis for this. Why is the amount of light absorbed proportional to the light that is present? If there are more light absorbing molecules present in solution, why don't they simply 'suck up' all of the light that is available to them. Why isn't there a simple linear decrease in transmission i.e. double the number of light absorbing molecules, double the light absorbed.

many thanks in advance for your help

Note: i think i've added the wrong graph but the one i wanted looks the same but just says % transmission down the y axis

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# Homework Help: UV spectrospscopy and exponential decrease in light transmission with concentration

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