discussed from now on The UV/VIS absorption is the principle of all the methods that will be discussed from now on The **Beer**-**Lambert** **law** This decrease of the radiation intensity can be expressed as: T = I/I 0 T is called transmittance and varies from/ A is measured at this λ max by the corresponding ε max λ [nm] Absorbance (relative units) λ 1 max λ 2 max Example 1: the **Beer**-**Lambert** **law** If we know ε (for the compound and given λ ) and the thickness of the absorbing layer (i.e. the width of a cuvette), we can /

and Matter Refraction Reflection Absorption Dr Huw Owens © Huw Owens - University of Manchester : Introduction Refraction of Light – Snell’s **Law** Surface Reflection of Light – Fresnel’s **Law** Absorption of light – **Beer**-**Lambert** **Law** © Huw Owens - University of Manchester : Refraction of Light – Snell’s **Law** Snell’s **Law** – When light travels through a medium of refractive index n 1 Encounters and enters a medium of refractive index n/

. Mechanism & wavelengths of light absorption. Spectrophotometers & the Biomate 3 Spectrophotometer. The **Beer**/**Lambert** **Law** in absorption sepectroscopy. Applications: Concentration determinations. Absorbance spectra. Enzyme kinetics. Introduce you /1 cm) Importance: since and l are both constants, absorbance is directly proportional to concentration. * The **Beer**/**Lambert** **Law** is often referred to a “**Beer**’s **Law**”. A = cl where: is the molar extinction coefficient (liters/mole cm) c = the/

during its passage through the absorbing medium is governed by two **laws** : **Lambert**’s **law** and **Beer**’s **law**. In the combined form they are referred to as the **Beer**-**Lambert** **law**. **Lambert** **law** **Lamberts** **law** stated that absorbance of intensity of a light by material sample/pass through an identical cell, only 25 will emerge, and so forth. Transmittance and path length—the Bouguer-**Lambert** **law** **Lambert** (1760) generally is credited with the first mathematical formulation of this effect, although it now appears that Bouguer /

of an absorbing solute (path length of light) and the concentration. It is a combination between **Beer**’s **law** and **lambert**’s **law**. **Laws** of Light Absorption **Beer**’s - **Lambert**’s **Law**: Log I o / I t = a b C Log I o / I t = /weight A 1% 1cm [1] Real deviation: In high concentration due to crowding, molecules interaction & association. **Laws** of Light Absorption Deviations from **Beer**’s - **Lambert**’s **Law**: (b) Regular deviation due to slit width control, stray light is indefinite wavelength, also any light reaches the/

solution in cm-1 A = absorbance = log(Io/I) ℓ 0.1 cm http://www.hellma-worldwide.de/en/default.asp **Beer**-**Lambert** **Law** A Absorbance or optical density (OD) e absorptivity; M-1 cm-1 c concentration; M T transmittance Transmittance, Absorbance, and Cell/ Pathlength http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/beers1.htm Deviations from the **Beer**-**Lambert** **Law** Low c High c The **Beer**-**Lambert** **law** assumes that all molecules contribute to the absorption and that no absorbing molecule is in the shadow of/

on a single carbon source –Growth on a two carbon sources (diauxic growth/catabolite repression) Experiments for today Spectrophotometry: The **Beer**-**Lambert** **law** Relates concentration to the optical measurement of ‘absorbance’ –Example: E. coli concentration Combined with spectrophotometry can be used to/: dI z /I z =-σ·c·dz I 1 (λ) = I 0 e -σ(λ)·c· l = I 0 10 -ε(λ)·c· l z σ The **Beer**-**Lambert** **law** I 0 = incident light ( W/cm^2) c = Number density of absorbers (e.g. cells) σ(λ) = particle cross section (cm^2)/

experiment here: UV-Visible + IR Spectroscopic Methods Introduction to the Principles of Spectroscopy Quantitative Analysis with **Beer**-**Lambert**’s **Law** **Beer**-**Lambert** **law** relates absorption of light to concentration of a chemical A = ε l C Where A = absorbance/46 x 1000 UV-Visible + IR Spectroscopic Methods Introduction to the Principles of Spectroscopy Quantitative Analysis with **Beer**-**Lambert**’s **Law** UV-Visible + IR Spectroscopic Methods UV-Visible Spectroscopy UV-Visible Instrumentation 5 major components: –(1)/

a colorimetric method to be quantitative, it must form a coumpound with definite color characteristics. Color amount must be directly proportional to the concentration. Colored compound must obey **Beer**’s **Law** and **Lambert**’s **Law**. **Lambert**’s **Law** Relates the absorption of light to the depth or thickness of the colored liquid. Each layer of equal thickness absorns an equal fraction of the light which traverses/

coefficient. Integrating yields: K. N. Liou This relation is known as **Beer**–**Lambert** **Law** (after August **Beer** and Johann Heinrich **Lambert**) – which has been discovered by – Pierre Bouguer. **Beer**–**Lambert**–Bouguer **Law** Atmo II 102 With the definition of the optical thickness: In atmospheric applications/factor. For the plan-parallel case it is simply 1/cosθ. Alternative formulations of the **Beer**–**Lambert** **Law** use cross sections, e.g.: **Beer**–**Lambert**–Bouguer **Law** Atmo II 103 where N is the number density (unit m –3 ). The /

. Its main function is to measure the absorbance or concentration of substances. **Beer**-**Lambert** **Law**: **Beers** **Law** states that: when a ray of monochromatic light passes through an absorbing medium, the intensity decreases as the /, its intensity decreases as the length of the medium increases. These two **laws** are combined in the form of **Beer**- **Lambert** **Law** and expressed as: A = abc These two **laws** are combined in the form of **Beer**- **Lambert** **Law** and expressed as: A = abc Where: Where: A= Absorbance./

unit infinitesimal path length). The absorption coefficient can be considered as the total cross- sectional area for absorption per unit volume. Absorption The **Beer**-**Lambert** **law** (or **Beers** **law**) is the linear relationship between absorbance and concentration of an absorbing species. The general **Beer**- **Lambert** **law** is usually written as: A = a( λ ) * b * c where A is the measured absorbance, a( λ ) is a wavelength-dependent absorptivity coefficient, b/

radiation (a) 2 1 0 E 2 = h 2 = hc/ 2 E 1 = h 1 = hc/ 1 (b) A 2 1 0 (c) **Lambert** **Beer**’s **law** Transmittance T = P / P 0 %T = (P / P 0 ) 100 Absorbance (A, O.D., E, As) A = log T = log P/ P 0/ C log P/P 0 = ( /2.303) C A = log P/P 0 = ( /2.303) C **Lambert** - **Beer**’s **law** A = bC where is molar absorptivity Effect of concentration of analyte on transmittance and absorbance of light. A [C] log T Limitation **Beer**’s **law** 1. Concentration deviation ; A = log T = log P/P 0 = bC (Eq 1) (0.434 / T)/

: Below 200nm. Near UV region: 200nm- 400nm. Visible region: 400nm-800nm. 3 ELECTRONIC TRANSITIONS 4 . 5 **BEER**-**LAMBERT** **LAW** **BEER**-**LAMBERT** **LAW** When a beam of light is passed through a transperent cell containing solution of an absorbing substance, reduction in intensity of/ solution: ATR: 20 ppm NIACIN: 20ppm 22 Overlain spectra of ATR and NIACIN. 23 Result This method follows the **Beer** **lambert** **law** within range of 5-25 ppm. The overlain UV absorption spectra of ATR(246nm) and NIA(262nm) shows iso- absorptive/

metals? Alkali Metals in Water Accurate Lab - Spectrophotometry of Cobalt(II) Lab - Spectrophotometry of Cobalt(II) The **Beer** – **Lambert** Equation **Beer**’s **Law** **Beer** – **Lambert** **Law** The amount of light absorbed by a solution can be used to measure the concentration of the absorbing molecule in that solution by using the **Beer** – **Lambert** **Law**. **Beer** – **Lambert** **Law** A = Ɛ Cl where A is the absorbance, Ɛ is the molar absorption coefficient, C is the molar/

intensities Determining relative cloumn density measurements above the payload during the accent. Determining relative cloumn density measurements above the payload during the accent. **Beer**-**Lambert** **Law** **Beer**-**Lambert** **Law** **Beer**-**Lambert** **Law** In essence, the **law** states that there is an exponential dependence between In essence, the **law** states that there is an exponential dependence between the transmission of light through a substance and the concentration of the substance, and also/

/ nm Abs UV / visible Spectroscopy Electronic transitions involve the promotion of electrons from an occupied orbital to an unoccupied orbital. Energy differences of 125 - 650 kJ/mole. UV / visible Spectroscopy **Beer**-**Lambert** **Law** A = log(I O /I) = cl UV / visible Spectroscopy A = log(I O /I) = cl –A = Absorbance (optical density) –I O = Intensity of light on the sample cell –I = Intensity/

of appropriate ; pass light through sample; photocell detector measures intensity of light transmitted. I = I0e-kt **Beer**-**Lambert** **Law** Intensity of light transmitted through a sol’n falls exponentially as the path length (l) ↑. I =/ passing through sample I0= intensity of light before passing through sample k=absorbance of 1 cm pathlength sample l = pathlength I = I0e-kt **Beer**-**Lambert** **Law** 𝐴= 𝑙𝑜𝑔 10 𝐼 0 𝐼 =𝜀𝑐𝑙 Generally expressed in logarithms to base 10, with the ratio log10(I0/I) defined as the absorbance (/

very small volumes and flow-through cell (b) for automated applications Transmittance and Concentration The Bouguer-**Lambert** **Law** Transmittance and Path Length: **Beer**’s **Law** Concentration The **Beer**-Bouguer-**Lambert** **Law** **BEER** **LAMBERT** **LAW** As the cell thickness increases, the intensity of I (transmitted intensity of light ) decreases. /I I0 I I0 1 T I0 I I I0 A CL = KCL by definition and it is called the **Beer** **Lambert** **Law**. A = KCL K = Specific Extinction Coefficient ---- 1 g of solute per liter of solution A = ECL/

UV help to detect ozone? Absorption cross sections Absorption cross sections Ozone measurements Ozone measurements **Beer**-**Lambert**’s **Law** **Beer**-**Lambert**’s **Law** Discovery of UV Johann W. Ritter Johann W. Ritter 1801 projected sunlight through a/ amount of UV within a specified wavelength range Using a longer wavelength sensor Using a longer wavelength sensor **Beer**-**Lambert** **Law** **Beer**-**Lambert** **Law** **Beer**-**Lambert** **Law** Light transmission has an exponential dependence on: Concentration or thickness of the gas Path length/

with m/z = 26? (ii) Calculate the relative atomic mass of magnesium. Spectroscopy and the **Beer**-**Lambert** **Law** Spectroscopy - the study of the interaction of electromagnetic radiation and matter. Absorption spectroscopy methods involve a / be used to gather information about electronic configurations. **Beer**-**Lambert** **Law** The **Beer**-**Lambert** **law** is used to relate the concentrations of colored solutions to the amount of visible light they absorb. **Beer**-**Lambert** **Law** The amount of absorbance is calculated using the formula/

Histology – muscle Cell Types – Domains of Life Parasitology Infectious Prokaryote, Protista, and Fungi Photosynthesis Enzyme Kinetics CHEMISTRY Acid Base Titration Citric Acid in Popular Drinks - Titration Emission Spectroscopy **Beer**-**Lambert** **Law** **Beer**-**Lambert** **Law** of food dye in sports drinks Colligative Properties – Freezing Point Depression Electron Charge to mass ratio Gas Chromatography Enzyme Kinetics * These activities are under development, Underlined labs are used in /

l Harry Kroto 2004 Fermi’s Golden Rule IoIo I xx l **Beer** **Lambert** **Law** I= I o e - l Harry Kroto 2004 Fermi’s Golden Rule IoIo I xx l **Beer** **Lambert** **Law** I= I o e - l Harry Kroto 2004 Fermi’s Golden Rule **Beer** **Lambert** **Law** I= I o e - l IoIo I xx l /Harry Kroto 2004 Fermi’s Golden Rule **Beer** **Lambert** **law** I= I o e - l IoIo I xx l Harry /

Concentration This makes absorption spectroscopy one of the few bioanalytical methods where the signal intensity is directly proportional to the concentration Temperature (within reason) Absorption: The **Beer**-**Lambert** **Law** The **Beer**-**Lambert** **law** sortof has the wrong name… Pierre Bouguer (1698-1758) Johan **Lambert** (1728-1777) Astronomer: Light is diminished as it passes through the atmosphere. Mathematician, first to prove that is irrational. No absorption coefficient. August/

based are mainly absorption and transmission. In order to understand how, it is necessary to take **Beer** **Lambert**’s **law** into account. **Beer** **Lambert**’s **Law**. it identifies the relationship between the concentration of the sample and the intensity of light transmitted through/ how absorbance [A]and transmittance [T] vary as a function of the concentration [C] according to **Beer** **Lambert**’s **law**. Transmittance graph Absorbance graph In conclusion it can be inferred that by increasing the concentration of a substance,/

by radiation in the short wavelength UV region 29prof. aza 30prof. aza 31prof. aza **Beer**-**Lambert** **Law** prof. aza32 Fig. 4.3: Absorption of light by a solution 33prof. aza **Beer**-**Lambert** **Law** Figure 4.3 shows the absorption of radiation by a solution containing a UV- /absorbing compound. The measurement of light absorption by a solution of molecules is governed by the **Beer**-**Lambert** **Law**, which is written as follows: log Io/It =A= ε bc 34prof. aza where Io is the intensity of incident/

oxygen out of the lungs = cardiac output x (Arterial oxygen content – Mixed venous oxygen content) PULSE OXIMETRY **Beer** **Lambert** **Law** **Beer** **Lambert** **Law** Absorption of light = Concentration x Thickness x extinction coefficient Absorption of light = Concentration x Thickness x extinction coefficient/oxyhemoglobin At 940nm, little absorption by deoxyhemoglobin At 940nm, little absorption by deoxyhemoglobin PULSE OXIMETRY **Beer**’s **Law** states that the absorption of radiation by a given thickness of a solution of a given/

: A = -log T = log P 0 /P h P0P0 Sample (power in) P (power out) We don’t measure absorbance. We measure transmittance. The **Beer**-**Lambert** **Law** ( specific): A = absorbance (unitless, A = log 10 P 0 /P) = molar absorptivity (L mol -1 cm -1 ) l = path length/ = l( 1 c 1 + 2 c 2 + 3 c 3 ) A 1 = 1 c 1 l Limitations to Bear’s **Law** Reflection/Scattering Loss The **Beer**-**Lambert** **Law**: A = c l A = -log T = log P 0 /P Reflection/Scattering - Air bubbles - Aggregates Lamp effects - Temperature (line broadening)/

T=1=100% , P=P0 and A=0 I= I0 and A=0 2008-11-19 Monochromatic light **Lambert** – **Beer**,s **law**, commonly called **Beers** **law**: Absorbance is directly proportional to the concentration of light-absorbing species in the sample and the pathlength of the solution. **Lambert**–**Beer**,s **law** is strictly valid for purely monochromatic radiation; that is, for radiation consisting of only one wavelength. Monochromatic light/

is proportional to number of absorbing particles in volume of a solution, that is concentration Bouguer-**Lambert**-**Beer** **law** Reduction of intensity of light which has passed through a layer of light-absorbing substance is/(Absorbance) An alternative method for expressing the attenuation of electromagnetic radiation is absorbance, A, which is defined as or Bouguer-**Lambert**-**Beer** **law** So: The absorbance of a solution is proportional to concentration of light-absorbing substance and a thickness of a layer /

T = P/P o P o : incident light power P : transmitted light power %T = P/P o x 100 =……… % Absorbance A = - log T **Beer**’s-**Lambert** **law** A =absorbance b = pathlength (cm) c =concentration A = abC where a is the analyte’s absorptivity with units of cm –1 conc –1. If we express /be stable with time 4.The reaction of its formation, must be rapid and quantitative. 5-The colored product, should obey **Beer**-**lambert**’s **law**, i.e on plotting A versus C at fixed b, we obtain straight line passing through the origin.

– the amount of incident radiation absorb by the medium and expressed by: A = log(1/T) = - logT = log P0/P **BEER** **LAMBERT** **LAW** As the cell thickness increases, the intensity of I (transmitted intensity of light ) decreases. T- Transmittance T = I0 - Original light / fraction of transmitted radiant energy b – the pathlength of the medium A CL = KCL by definition and it is called the **Beer** **Lambert** **Law**. A = KCL K = Specific Extinction Coefficient ---- 1 g of solute per liter of solution A = ECL E = Molar /

absorption of certain functional groups bands is directly proportional to the concentration of the substance and obeys Bear’s-**Lambert** **law** Quantitative IR Spectroscopy FT-IR instruments have virtually overcome the accuracy and instrumental limitations referred to in (2) / absorbance and percentage transmission just as they are in UV-VIS electronic spectra, and so, they obey **Beer**-**Lambert** relationship It has taken a long time for quantitative infrared spectrophotometry to become a commonly used procedure for /

substance to be anaylsed is dissolved Therefore, under experimental conditions. Io = Ia + It or Ia = Io - It Lecture V 1-**Beer**-**Lambert** **Law** 2-Absorptivity , Molar absorptivity and A1%.1cm % Transmittance %T = 100 x T Transmittance T = It / Io The diagram below shows/stable with time 4.The reaction of its formation, must be rapid and quantitative. 5-The colored product, should obey **Beer**-**lambert**’s **law**, i.e on plotting A versus C at fixed b, we obtain straight line passing through the origin. Instrumentation The/

(A is a ratio and therefore has no units) The constant E is called the MOLAR EXTINCTION COEFFICIENT Link to “**Beer**-**Lambert** **law**” video This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License UV/ Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales License UV / VISIBLE SPECTROSCOPY - THEORY IMPORTANCE OF THE **BEER** **LAMBERT** **LAW** A = Ecl but if E and l are constant ABSORBANCE CONCENTRATION and should be linear relationship Prepare standards of/

Correlation comparing infrared energy absorbed by a sample to that absorbed by a reference gas according to the **Beer**-**Lambert** **law**. the **Beer**-**Lambert** **law** The **law** states that there is a logarithmic dependence between the transmission T of light through a substance and the/Filter Correlation comparing infrared energy absorbed by a sample to that absorbed by a reference gas according to the **Beer**-**Lambert** **law**. This is accomplished with a Gas Filter wheel which alternately allows a high energy light source to pass /

be stable with time. 4- The reaction of its formation, must be rapid and quantitative. 5- The colored product, should obey **Beer**-**lambert**’s **law**, i.e on plotting A versus C at fixed b, we obtain straight line passing through the origin. 37 38 A- Visual methods/ mixture, the following requirements must be fulfilled: 1-The absorption spectrum of X and Y should not show sever overlap. 2-**Beer**-**Lambert** ’ s **law** must be obeyed for X and Y at their characteristic max. 3-X and Y must be chemically inert to each other./

log (1/T) = log(100/%T) Transmittance Transmittance defined as T = P P0P0 Thus 22 Relationship between Absorbance and Concentration **Beer**-**Lambert** **Law** A = l c Where: path length in cm l is the path length in cm concentration c is the concentration in/ mol/L molarabsorptivity is the molar absorptivity 23 Applications of the **Beer**-**Lambert** **Law** Analysis of a single analyte 1.Measure absorbance of a series of standard solutions 2.Plot a standard curve (should/

the sample I = the intensity of light after pass through the sample The absorbance (A) can be linked to a **law** known as the **Beer**-**Lambert** **law** (which can be found in section 1 of the IB data booklet) A = log 10 (I 0 /I) RSC - / moldm -3 solution in a 1.00 cm cell at a specified wavelength Concentration of the solution, c Path length, l The **Beer**-**Lambert** **law** is expressed as: “ The absorbance of a compound is directly proportional to its concentration (at a fixed wavelength)” UV-vis Spectrophotometer Video/

attenuation of light, from the light beam (source) to the photodetector (signal), is typically modeled by the **Beer**- **Lambert** **law**. This **law** states that in a homogeneous medium, light intensity decays exponentially as a function of path length (l) and /surface as well as other physical processes (e.g., light scattering) are not contemplated by this model. The **Beer**-**Lambert** **law** helps in understanding the absorbance of light traveling through homogeneous layers. However, the blood and other biological tissues /

power out) Transmittance: T = P/P0 Absorbance: A = -log10 T = log10 P0/P B(path through sample) The **Beer**-**Lambert** **Law** (a.k.a. **Beer**’s **Law**): A = ebc Where the absorbance A has no units, since A = log10 P0 / P e is the molar absorbtivity /in cm c is the concentration of the compound in solution, expressed in mol L-1 (or M, molarity) **Beer**-**Lambert** **Law** Linear absorbance with increased concentration--directly proportional Makes UV useful for quantitative analysis and in HPLC detectors Above a certain concentration /

as the negative logarithm of the transmittance This means that, as the concentration of the absorbing species increases, the amount of transmitted light decreases, and therefore, the absorbance increases The **Beer**-**Lambert** **Law** Let’s think about this for a bit… If we increase the distance the light travels through the solution, the amount of light absorbed should increase. This distance is called/

Solis’s Margin Comments What about the biuret reagent? How is this useful? How does the spectrophotometer work? What is the **Beer**-**Lambert** **Law**? Explain in greater detail. Breaking Down the Components Introduction, Materials, Methods, Data & Results, Conclusion & Discussion, Graphs & /I state the general purpose of the lab in the Introduction? Where should I explain how I used the **Beer**-**Lambert** **Law** to construct a standard curve? What goes in the “Discussion” section? Sample Student Conclusion Because the data /

composite data by making more mixtures with differing amounts of reactants. Model all the data according to chemical equilibria and the **Beer**-**Lambert** **law** for combining absorbances. Why it Works Each data point corresponds to a single equation. For each point on the same/ absorbance at any particular point is the sum of the absorbances of all the chemical species in solution according to **Beer**-**Lambert** **Law**. Molar Absorptivities (n x m) Every column represents one of the m chemical species. Every row is/

SO2 analysis techniques. Monitoring System System Details Advantages Disadvantages Simple non-dispersive Infrared (NDIR) Based on **Beer** **Lambert** **Law**. Low cost. Reliable. Suffers interferences from CO2 and H2O Luft Detector (NDIR) Works on same basis/to measurement. Differential Optical Absorption Spectroscopy - DOAS Applicable to extractive & in situ systems Method principle is **Beer**-**Lambert** **Law**. Light of different length is transmitted across emission stack. Light wavelength are selected using – diode laser, /

being analyzed Tubes or cuvettes Visible range = glass cuvette UV range = quartz cuvette Photocell To detect transmitted light Spectrophotometry **Beer**-**Lambert**’s **Law** lo g Io = cl I Where: Io = intensity of incident light I = intensity of transmitted light / compound under standard conditions b = light path of the solution c = concentration of the compound %T = percent transmittance **Beer**-**Lambert**’s **Law** Absorbance A = K x C = Log10Io I Where: Io = amount of light absorbed by the solution expressed as absorbance/

a kind of finger print The absorbance is proportional to the concentration 11 Video of absorption 12 **Lambert**-**Beer**’s **law** Converting absorbance into concentrations Measured absorbance of a single substance is directly proportional to its concentration and the/ extinction coefficient of substance y at wavelength = concentration of substance y in sample = length of light path **Lambert**-**Beer**’s **law** Measured absorbance of a single substance is directly proportional to its concentration lA yyy c Note that /

with a UV-Vis Spectrophotometer Practice several analytical techniques Understand absorbance and application of the **Beer**-**Lambert** **Law** Background: Absorption of Radiation Absorption – A process in which electromagnetic energy is transferred/ion Most ions are singly charged Molecular Absorption Measurement of Transmission and Absorption Limitations to **Beer**-**Lambert** **Law** –Concentration –Chemical deviations –Polychromatic Radiation Fluorescence and Phosphorescence Following absorption –Nonradiative relaxation Loss /

Pediatric Resident Curriculum for the PICU INFRARED First developed in 1859. First developed in 1859. Based on **Beer**-**Lambert** **law**: Pa = 1 - e - DC Based on **Beer**-**Lambert** **law**: Pa = 1 - e - DC – Pa is fraction of light absorbed – / UTHSCSA Pediatric Resident Curriculum for the PICU PULSE OXIMETRY Uses spectrophotometry based on the **Beer**- **Lambert** **law** Uses spectrophotometry based on the **Beer**- **Lambert** **law** Differentiates oxy- from deoxyhemoglobin by the differences in absorption at 660nm and 940nm Differentiates/

then obtained with the equation: A = log P solvent /P solution x log P o /P **Beer**’s **Law** Bouguer, and later **Lambert**, observed that the fraction of the energy, or the intensity, of radiation absorbed in a thin layer / thickness, leads to an exponential relationship between transmitted intensity and thickness. **Beer**’s **Law** (cont) **Beer** showed that, at a given thickness, the absorption coefficient introduced by **Lambert**’s **law** was directly proportional to the concentration of the absorbing substance in a solution/

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