158. THE LAWS OF PHOTOCHEMISTRY (4).

Absorbance

In the previous post, we introduced the term absorbance. The term absorbance quantifies the amount of light absorbed by a solution. We know from the previous post –

We stated that absorbance and transmittance are two sides of a coin. How are they related?

Absorbance is commonly expressed in terms of I_o and I_t, as follows –

The following table gives the values for both A and T –

In mathematics, a logarithm means the opposite of an exponential.

In simple terms, log _b x = y means b^y = x
Thus, log ₁₀ x = y means 10 ^y = x
e.g. – log ₁₀ 1000 = 3 means 10 ³ = 100

Also , – log (x) = log (1/x)

It’s not important, but just for your information, we can derive this expression as follows –

Graphically the relationship between A and T can be shown as –

How to understand this graph?

The blue line indicates that as the absorbance(A) decreases, the %T value increases. This is because both those terms are inversely proportional. However, this inverse relationship is NOT linear but a logarithmic one –
e.g – If 50% of the photons of monochromatic light are transmitted by a sample, and 50% of the photons are absorbed, T = 0.5, but A is not 0.5, A is 0.3 (inverse logarithmic relationship between T and A). 

The above graph also corroborates the relationship –

A = log ₁₀ (1/T)

The difference between the graphs of expressions y= log ₁₀ (x) and y= log ₁₀ (1/x) is shown below –

Transmittance and absorbance have no units. The term optical density is an older term for absorbance and is no more used by the scientific world.

After studying the terms absorbance and transmittance and the Beer – Lamberts’s law, we shall proceed to discuss the next law of photochemistry in the next post. Till then,

Be a perpetual student of life and keep learning….

Good day!

References and further reading –

1.Physical Chemistry by W J Moore, the first edition

2.http://stevegallik.org/cellbiologyolm_spectrophotometry.html