Carbon dioxide peril

Being a science graduate, I would expect to be able to understand how the Greenhouse Effect works, but have not seen a convincing explanation for how a concentration of one part in 2,500 of the gas can have such a disproportionate effect. The greenhouse effect theory has been around for over a century, when it was first noted by the Swedish chemist, Arrhenius. However, carbon dioxide absorbs infrared radiation (IR) in three narrow bands of wavelengths, which are 2.7, 4.3 and 15 micrometers (µM). This means that most – about 92% – of the heat producing radiation escapes it. About 8% of the available black body radiation is picked up by these characteristic frequencies of CO2.

Can someone please explain how a concentration of 1 part of carbon dioxide in 2500 can cause a greenhouse effect?

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