How to find reduction in light intensity
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How to find reduction in light intensity

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
875 m⁻¹ ] [ 2.5 × 10⁻³ m ] = 0.…I / I₀ = 10^(‒αL) = 10^(‒0.6946875) = 0.......
The molar absorption coefficient of a substance dissolved in water is known to be 855 dm3 mol-1 cm-1 at 270 nm. To determine the rate of decomposition of this substance, a solution with a concentration of 3.25 mmol dm-3 was prepared. Calculate the percentage reduction in intensity when light of that wavelength passes through 2.5 mm of this solution.

Using Beer's Law
I found that I/I. = .984
The Sol. Manual says the percentage reduction in intensity is 100%-20.2% = 79.8%

Not sure how to get from .984 to 79.8%

-
Given is the molar absorptivity ε and not the molar absorption coefficient α, which
is measured in meter⁻¹ in SI system. If you don’t know what a given quantity is, look
carefully at the unit of that quantity. That is why knowing the unit of every quantity
is important.
… ε = 855 dm³ • mol⁻¹ • cm⁻¹ = 855 [ 10⁻¹m ]³ • mol⁻¹ • [ 10⁻²m] ⁻¹
……= 855 × 10⁻³ × 10² m² mol⁻¹ = 855 × 10⁻¹ m² mol⁻¹
…… = 85.5 m² • mol⁻¹
… L = 2.5 mm = 2.5 × 10⁻³ m
… α = εc ---> α = [ 85.5 m² • mol⁻¹ ] [ 3.25 mol • m⁻³ ] = 277.875 m⁻¹
… αL = [ 277.875 m⁻¹ ] [ 2.5 × 10⁻³ m ] = 0.6946875
… I / I₀ = 10^(‒αL) = 10^(‒0.6946875) = 0.202
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