Method of Experimental Physics

Course No: PH -404

Chapter-1
Optical and spectroscopy instruments

iii. Spectrophotometer

©Prof. Dr. M. Mizanur Rahman

 Spectrophotometer
The word spectrophotometer is derived from the Latin word spectrum, which
means image, and the Greek word phos or photos, which means light.

Generally, light from a lamp with special characteristics is guided through a

device, which selects and separates a determined wave length and makes it pass
through a sample.

The light intensity leaving the sample is captured and compared with that
which passed through the sample.

Transmittance, which depends on factors such as the substance concentration is

calculated from this intensity ratio.
 SPECTROPHOTOMETER
A spectrophotometer is an instrument that measures the amount of photons
(the intensity of light) absorbed after it passes through a sample. With the
spectrophotometer, the amount of a known chemical substance
(concentrations) can also be determined by measuring the intensity of light
detected.

How it works….
1. Direct a light beam onto an object.

2. Receiving the light reflected or

returned from the object.

3. Detecting the intensities with a

charge-coupled device.

4. Displaying the results as a graph

on the detector and then the
display device.
 SPECTROPHOTOMETRY
➢ Spectrophotometry is a branch of electromagnetic spectroscopy
concerned with the quantitative measurement of the absorbance,
reflection or transmission properties of a material as a function of
wavelength.
➢ Compounds absorb light of a specific wavelength.
➢ The amount of light absorbed by a sample is measured.
➢ The light absorption is directly related to the concentration of the
compound in the sample.
➢ As concentration increases, light absorption increases linearly. As
concentration increases, light transmission decreases consequently.
 TYPE OF SPECTROPHOTOMETER

Depending on the range of wavelength of light source, it can be classified into

two different types:
UV-visible spectrophotometer: uses light over the ultraviolet range (185 - 400
nm) and visible range (400 - 700 nm) of electromagnetic radiation spectrum.
IR spectrophotometer: uses light over the infrared range (700 - 15000 nm) of
electromagnetic radiation spectrum.
• In visible spectrophotometry, the absorption or the transmission of a certain
substance can be determined by the observed color.
• For instance, a solution sample that absorbs light over all visible ranges (i.e.,
transmits none of visible wavelengths) appears black in theory.
• On the other hand, if all visible wavelengths are transmitted (i.e., absorbs
nothing), the solution sample appears white.
• If a solution sample absorbs red light (~700 nm), it appears green because
green is the complementary color of red.
• Visible spectrophotometers, in practice, use a prism to narrow down a certain
range of wavelength (to filter out other wavelengths) so that the particular
beam of light is passed through a solution sample.
 PURPOSE OF SPECTROPHOTOMETER
✓ Measure the concentration of the solution:
1. A spectrophotometer optically determines the absorbance or transmission of
characteristic wavelengths of radiant energy (light) by a chemical species in
solution.
2. Each molecule absorbs light at certain wavelengths in a unique spectral
pattern because of the number and arrangement of its characteristic functional
groups, such as double bonds between carbon atoms.
3. According to the Beer-Lamberts law, the amount of light absorbed at these
wavelengths is directly proportional to the concentration of the chemical
species.
✓ Identify organic compounds by determining the absorption maximum:
Spectrophotometers are used to identify organic compounds by determining the
absorption maxima (which for most compounds and groups of compounds have
very distinct fingerprints that’s what the absorption curves and peaks are called)
✓ Band gap measurement
1. using Tauc relation
2. kubelka munk function
 PRINCIPLE OF SPECTROPHOTOMETER
Spectrophotometer is based on the photometric technique. A beam of incident light of
intensity I0 passes through a solution, a part of the incident light is reflected (Ir), a part is
absorbed (Ia) and rest of the light is transmitted (It)
Thus, I0 = Ir + Ia + It

Transmittance (T) = It/Io

Where It is the light intensity after the beam of light passes through the cuvette and Io is
the light intensity before the beam of light passes through the cuvette. Transmittance is
related to absorption by the expression:
Absorbance (A) = −log(T)= −log(It/Io) = log(I0/It)
Where absorbance stands for the amount of photons that is absorbed. With the amount of
absorbance known from the above equation, you can determine the unknown concentration
of the sample by using Beer-Lambert Law.
 PRINCIPLE OF SPECTROPHOTOMETER
The portion of light absorbed by a medium is governed by two laws, on which the
Spectrophotometer is based. These laws are,
1. Lambert’s Law
2. Beer’s Law
Lambert’s Law
➢ The Lambert’s law describes the relation between absorbance and thickness of the
absorbing materials and which is directly proportional.
➢ According to this law, when a beam of monochromatic light passes through of a
homogeneous absorbing medium, the rate of the decrease of the intensity of radiation
with thickness is proportional to the intensity of incident light.

Mathematically this can be expressed as, 𝑑𝐼

− αI
𝑑𝑥
𝑑𝐼
− = kI (1)
𝑑𝑥

Where, I = intensity of incident light

x= thickness of the absorbing medium
k= proportionality const.
# From Lambert’s law, show that intensity of incident light decrease
exponentially with the increase of the thickness of the absorbing medium?
And, also show that absorbance A=ЄX.

From eqn. (1)

𝑑𝐼
− = kI
𝑑𝑥
𝑑𝐼
− = kdx
𝐼

Integrating over 𝐼𝑜 to 𝐼𝑡 for x=0 to x=x,

𝐼𝑡 𝑑𝐼 𝑥
‫𝐼 𝐼׬‬ = -‫׬‬0 𝑘𝑑𝑥
0

ln(It/Io) = -kx (2)

It/Io = exp(-kx)

It = Io*exp(-kx)
(showed)
From eqn. (2),
ln(It/Io) = -kx

2.303log(It/Io)= -kx

-log(It/Io) = (k/2.303)*x

A=ЄX
Where,
A=-log(It/Io) = absorbance of the medium

Є= Molar extinction coefficient

Beer’s Law:
➢ The Beer’s law describes the relation between absorbance and concentration
of the solution medium and which is directly proportional.
➢ According to this law, when a beam of monochromatic light passes through
a homogeneous solution medium, the rate of the decrease of the intensity of
radiation with thickness is proportional to the concentration of the solution
medium.
 Beer-Lambert law
➢ Combination of both Lambert’s law and Beer’s Law for homogenous
absorbing solution.
Mathematically,
𝑑𝐼
− α I*C
𝑑𝑥

𝑑𝐼
= −𝑘*C*dx
𝐼

Integrating over 𝐼𝑜 to 𝐼𝑡 for x=0 to x=x,

𝐼𝑡 𝑑𝐼 𝑥
‫𝐼 𝐼׬‬ = -‫׬‬0 𝑘𝐶𝑑𝑥
0

ln(It/Io) = -kcx (2)

It/Io = exp(-kcx)
 It = Io*exp(-kcx)
From eqn. (2),
ln(It/Io) = -kcx

2.303log(It/Io)= -kcx

-log(It/Io) = (k/2.303)*cx

A=ЄCX
Where,
A=-log(It/Io) = absorbance of the medium

C= concentration of the solution

Є= Molar extinction coefficient

Molar extinction coefficient: measurement of absorbance for a

solution of concentration 1 mole per liter and thickness of 1 cm. it is
characteristics of solute and depends on solvent, temperature and
wavelength of incident light.
❑ Find the relative amount of light that gets absorbed by the sample if the
absorbance of the sample is 2 at a particular wavelength.

Solution:
According to the absorbance definition;
A = log10 (I0/ It)

Rearrange the equation to determine the relative loss of intensity

10A = I0/ It
10-A= It/I0
Substituting the value of A = 2

Ia / I0 = 1- It/I0 = 1 – 10-2 = 1 – 1/100 = 0.99

Therefore, we can say that 99% of the light is absorbed and 1% of light is
transmitted.
 EXAMPLES OF BEER-LAMBERT’S LAW

◆ Guanosine has a maximum absorbance of 275 nm. ϵ275=8400 M−1cm−1 and the path
length is 1 cm. Using a spectrophotometer, you find that A275=0.70. What is the
concentration of guanosine?
Solution: To solve this problem, you must use Beer's Law. A = ∈cl
 0.70 = (8400 M-1 cm-1)(1 cm)(c)
 c = 8.33x10-5 mol/L
◆ There is a substance in a solution (4 g/liter). The length of cuvette is 2 cm and only 50%
of the certain light beam is transmitted. What is the absorption coefficient? how much is
the beam of light is transmitted when 8 g/liter ? what is the molar absorption coefficient
if the molecular weight is 100?
Solution: Using Beer-Lambert Law, we can compute the absorption coefficient.
Thus, log(I0/It) = log (1.0/0.5) = A = ∈cl
 log (0.5/1.0) = (4 g/liter) (2 cm) ∈
 ∈ = 0.0376
 EXAMPLES OF BEER-LAMBERT’S LAW
the transmission, A= log(I0/It) = log(1)−log(It) = 0 − log(It) = 0.0376 x 8 x 2 = 0.6016
 log(It) = -0.6016,
 It = 0.2503 = 25%
∈ can simply obtained by multiplying the absorption coefficient by the molecular
weight. Thus, ∈ = 0.0376 x 100 = 3.76 L·mol-1·cm-1
◆ The absorption coefficient of a glycogen-iodine complex is 0.20 at light of 450 nm.
What is the concentration when the transmission is 40 % in a cuvette of 2 cm?
Solution
It can also be solved using Beer-Lambert Law.
log(I0/It) = log (1.0/0.4) = A = ∈cl
 log(1.0/0.4)=0.20×c×2
 c = 0.9948
 DEVICES AND MECHANISM
Figure illustrates the basic
structure of
spectrophotometers. It
consists of a light source,
a collimator, a
Monochromator, a
wavelength selector, a
cuvette for sample
solution, a photoelectric
detector, and a digital
display or a meter.

Figure shows a sample

spectrophotometer
(Model: Spectronic 20D).
 DEVICES AND MECHANISM
A spectrophotometer, in general, consists of two devices; a spectrometer and a photometer.
A spectrometer is a device that produces, typically disperses and measures light. A
photometer indicates the photoelectric detector that measures the intensity of light.
Spectrometer: It produces a desired range of wavelength of light. First a collimator (lens)
transmits a straight beam of light (photons) that passes through a monochromator (prism)
to split it into several component wavelengths (spectrum). Then a wavelength selector
(slit) transmits only the desired wavelengths.
Photometer: After the desired range of wavelength of light passes through the solution of
a sample in cuvette, the photometer detects the amount of photons that is absorbed and
then sends a signal to a galvanometer or a digital display.
Spectrophotometers come in a variety of shapes and sizes and have multipurpose uses to
them. The different types of spectrophotometers available are all different from one
another, based on their application and desired functionality. The most popular
spectrophotometers are 45 degrees, sphere and multi-angle spectrophotometers.
INTERNAL COMPONENTS OF SPECTROPHOTOMETER
 PARTS OF SPECTROPHOTOMETER
There are 6 essential parts of a spectrophotometer
1. Light source – In spectrophotometer three different sources of light are commonly used
to produce light of different wavelength. The most common source of light used in the
spectrophotometer for the visible spectrum is a tungsten lamp. For Ultraviolet
radiation, commonly used sources of are the hydrogen lamp and the deuterium
lamp. Nernst filament or globar is the most satisfactory sources of IR (Infrared) radiation.

Tungsten lamp
Tungsten Halogen lamp – It is the most common light source used in spectrometer. This
lamp consists of a tungsten filament enclosed in a glass envelope, with a wavelength range
of about 330 to 900 nm, are used for the visible region. They are generally useful for
measuring moderately dilute solutions in which the change in color intensity varies
significantly with changes in concentration. It has long life about 1200h.
 PARTS OF SPECTROPHOTOMETER
Hydrogen/Deuterium lamps – For the ultraviolet region, hydrogen or deuterium lamps
are frequently used. Their range is approximately 200 to 450 nm. Deuterium lamps are
generally more stable and has long life about 500h. This lamp generates continuous or
discontinuous spectral.

Xenon flash lamps – Xenon flash lamps have several advantages as the following:
1. Their range between (190 nm – 1000 nm)
2. Emit both UV and visible wavelengths
3. Long life
4. Do not heat up the instrument
5. Reduce warm up time.
 PARTS OF SPECTROPHOTOMETER

2. Dispersion devices:
A special plate with hundreds of
parallel grooved lines. The grooved
lines act to separate the white light
into the visible light spectrum. The
more lines the smaller the wavelength
resolution.

Monochromator – To select the particular

wavelength, prism or diffraction grating is used to
split the light from the light source. It accepts
polychromatic input light from a lamp and outputs
monochromatic light. Monochromator has entrance
slit, collimating lens or mirror, dispersion element,
focusing lens or mirror and exit slit.
 PARTS OF SPECTROPHOTOMETER
Types of dispersion devices:
Prism –
• Prism is used to isolate different wavelength. If a parallel beam of radiation falls on
a prism, the radiation of two different wavelength will be bent through different
angles.
• Prism may be made of glass or quartz. The glass prisms are suitable for radiation
essentially in the visible range whereas the quartz prism can cover the ultraviolet
spectrum also.
• It is found that the dispersion given by glass is about three times that of quartz.
Filter
Filters separate different parts of the electromagnetic spectrum by absorbing or
reflecting certain wavelengths and transmitting other wavelengths.
Absorption filters are glass substrates containing absorbing species that absorb certain
wavelength. A typical example is a cut on color filter, which blocks short wavelength
light such as an excitation source, and transmits longer wavelength light such as
fluorescence that reaches a detector.
Interference filters are made of multiple dielectric thin films on a substrate. They use
interference to selectively transmit or reflect a certain range of wavelengths. A typical
example is a Bandpass interference filter that transmits a narrow range of wavelengths
and can isolate a single emission line from a discharge lamp.
 PARTS OF SPECTROPHOTOMETER
Diffraction gratings
• Diffraction grating is an optical component with a regular pattern, which splits
(diffracts) light into several beams travelling in different directions. The
directions of these beams depend on the spacing of the grating and the
wavelength of the light so that the grating acts as a dispersive element.
• The diffraction grating disperses the light into a linear spectrum of its component
wavelengths, which is then directed, in whole or in part along the light path of
the instrument.
3. Focusing devices:
Combinations of lenses, slits and mirrors. It relay and focus light through the instrument.
Variable slits also permit adjustments in the total radiant energy reaching the detector.
PARTS OF SPECTROPHOTOMETER
Optical materials
Mirrors
Types of rays Mirror materials

X-rays- Ultraviolet (UV) Aluminum

Visible Aluminum

Near infrared Gold

Infrared (IR) Copper or gold

Lenses
Types of rays Mirror materials

X-rays- Ultraviolet (UV) Fluid silica, sapphire

Visible Glass

Infrared (IR) Glass

 PARTS OF SPECTROPHOTOMETER
4. Sample holder – Test tube or Cuvettes are used to hold the colored solutions. They
are made up of glass at a visible wavelength.
Cuvettes:
• It is designed to hold samples for spectroscopic
experiments made of plastic, glass or optical
quartz.
• It should be as clear as possible, without
impurities that might affect a spectroscopic
reading.
• It is usually a small square tube sealed at one end. Like a test-tube, a cuvette may be open
to the atmosphere on top or have a glass or Teflon cap to seal it shut.
• Cuvettes are chosen for transparency in the spectral wavelengths of interest. For
measurement in the visible region cuvettes of optical glass are sufficient; however, optical
glass absorbs light below 350 nm, and more expensive quartz or fused silica must be used
for these wavelengths. The sample cuvettes are placed in a darkened analysis chamber;
some chambers have rotating carousels that can hold several cuvettes.
 PARTS OF SPECTROPHOTOMETER
5. Detectors:
• it can convert radiant energy (photons) into as electrical signal. The photocell and
phototube are the simplest photodetectors, producing current proportional to the
intensity of the light striking them. When light falls on the detector system, an electric
current is generated that reflects the galvanometer reading.
• Any photosensitive device can be used as a detector of radiant energy.

There are two types of detectors.

Silicon pin photodiodes photovoltaic V-series: blue
enhances for spectral range from 350 nm to 1100 nm;
designed for low-noise, D.C. to medium bandwidth Photomultiplier tube Detectors

applications. Active areas range from 0.31 mm2 to 100 mm2.

applications include: low light level measurements, particle
counting, chemical and analytical measurement and detection.
 PARTS OF SPECTROPHOTOMETER
Gallium Nitride (GaN) UV detectors: This family of
Gallium Nitride (GaN) UV detectors are Schottky processed
fully passivated U.V. photodiodes. Spectral range from 200
nm to 365 nm and is ideal for UVA(315-400 nm) or
UVB(280-314 nm) sensing applications and is packaged with
a quartz window.

Beam splitter – It is present only in double beam spectrophotometer. It is used to split the
single beam of light coming from the light source into two beams.
Bandpass filter – It is a device that passes frequencies within a certain range and rejects
frequencies outside that range.
Mirror – It is also present only and double beam spectrophotometer. It is used to the right
direction to the splitted light from the beam splitter.
 PARTS OF SPECTROPHOTOMETER
6. Display devices – The data from a detector are displayed by a readout device, such
as analog meter, a light beam reflected on a scale, or a digital display, or liquid crystal
display (LCD). The current from the detector is fed to the measuring device – the
galvanometer. The meter reading is directly proportional to the intensity of light. The
output can also be transmitted to a computer or printer.
 HOW DOES A SPECTROPHOTOMETER WORK?
• First put the sample into a cuvette, then the light source generates light at a
specific wavelengths and the light passes through the dispersion devices that
separate the light into its components wavelengths.
• Then isolate the wave lengths needed for measurement with a bandpass filter to
improve its purity.
• The light passes through the
sample and a portion of
radiant energy absorbed. The
remaining light is transmitted
to the photometer, which
convert light energy to
electrical energy can be
registered on a meter.

• The amount of light absorbed depends on the nature of the concentration of the
sample.
 TYPES OF SPECTROPHOTOMETER
Spectrophotometer can be classified into two different types:
Single beam spectrophotometer operates between 325 nm to 1000 nm
wavelength using the single beam of light. The light travels in one direction
and the test solution and blank are read in the same. To measure the intensity
of the incident light the sample must be removed so that the reference can be
placed each time. This type of spectrophotometer is usually less expensive and
less complicated.

Single beam spectrophotometer

 TYPES OF SPECTROPHOTOMETER
Double beam spectrophotometer operates between 185 nm to 1000 nm wavelength. It
has two photocells. This instrument splits the light from the Monochromator into two
beams before it reaches the sample. One beam is used for reference and the other passes
through the sample for reading. This gives an advantage because the reference reading
and sample reading can take place at the same time. It eliminates the error which occurs
due to fluctuations in the light output and the sensitivity of the detector. This type of
spectrophotometer is usually expensive and complicated.

Double beam spectrophotometer

 WORKING PRINCIPLE OF THE
SPECTROPHOTOMETER

When using a Spectrophotometer, it requires being calibrated first which is done by

using the standard solutions of the known concentration of the solute that has to be
determined in the test solution. For this, the standard solutions are filled in the Cuvettes
and placed in the Cuvette holder in the spectrophotometer.

⇒ There is a ray of light with a certain wavelength that is specific for the assay is directed
towards the solution. Before reaching the solution the ray of light passes through a series
of the diffraction grating, prism, and mirrors. These mirrors are used for navigation of the
light in the spectrophotometer and the prism splits the beam of light into different
wavelength and the diffraction grating allows the required wavelength to pass through it
and reaches the Cuvette containing the standard or Test solutions. It analyzes the reflected
light and compares with a predetermined standard solution.
 WORKING PRINCIPLE OF THE
SPECTROPHOTOMETER
⇒ When the monochromatic light (light of one wavelength) reaches the Cuvette
some of the light is reflected, some part of the light is absorbed by the solution
and the remaining part is transmitted through the solution which falls on the
photodetector system. The photodetector system measures the intensity of
transmitted light and converts it into the electrical signals that are sent to the
galvanometer.

⇒ The galvanometer measures the electrical signals and displays it in the digital
form. That digital representation of the electrical signals is the absorbance or
optical density of the solution analyzed.
 WORKING PRINCIPLE OF THE
SPECTROPHOTOMETER
⇒ Absorption of the solution is higher means more light absorbed by the solution and
if the absorption of the solution is low, that means more lights will be transmitted
through the solution which affects the galvanometer reading and corresponds to the
concentration of the solute in the solution. By putting all the values in the formula we
can easily determine the concentration of the solution.

⇒ In double beam spectrophotometers, the beam splitters are present which splits the
monochromatic light into two beams one for the standard solution and the other for
test solution. In this, the absorbance of Standard and the Test solution can be measured
at the same time and any no. of test solutions can be analyzed against one standard. It
gives more accurate and precise results, eliminates the errors which occur due to the
fluctuations in the light output and the sensitivity of the detector.
 Band gap Measurement

1. From absorbance spectrum

Relation for measuring the band gap from absorbance spectrum is known as
Tauc relation. The relation is given by,

𝛼ℎ𝑣 = 𝐴(ℎ𝑣 − 𝐸𝑔 )𝑛
where, 𝛼, ℎ𝑣, A, 𝐸𝑔 and n represent the absorption coefficient, incident photon
energy, characteristic parameter independent of the photon energy, optical band
gap, and the electronic transition type, respectively. For direct and indirect
transitions, n were 0.5 and 2, respectively
 Band gap Measurement
2. From reflectance spectrum
The function which is used to measure band gap from reflectance spectrum
is known as Kubelka-Munk function. Which is given by,

where, K denotes the absorption coefficient (twice the Beer and Lamberts law
absorption coefficient), S is twice the scattering coefficient of the sample, ∈ is
the absorptivity, and C is the analytic concentration.
And, relation to the band gap is,

F(R)ℎ𝑣 = 𝐴(ℎ𝑣 − 𝐸𝑔 )𝑛

n= 1/2 for direct band gap

n=2 for indirect band gap
 APPLICATIONS
• Detection of concentration of substances
• Detection of impurities
• Structure elucidation of organic compounds
• Monitoring dissolved oxygen content in freshwater and marine
ecosystems
• Characterization of proteins
• Detection of functional groups
• Respiratory gas analysis in hospitals
• Molecular weight determination of compounds
• The visible and UV spectrophotometer may be used to identify
classes of compounds in both the pure state and in biological
preparations.
 PROBLEMS
1. A solution of Tryptophan (trp) has an absorbance at 280 nm of 0.54 in a 0.5 cm length cuvette.
Given the absorbance coefficient of trp is 6.4 × 103 LMol-1cm-1. What is the concentration of
solution?

2. A solution of thickness 2 cm transmits 40% incident light. Calculate the concentration of the
solution, given that ε = 6000 dm3Mol-1cm-1.

3. A solution shows a transmittance of 20%, when taken in a cell of 2.5 cm thickness. Calculate its
concentration, if the molar absorption coefficient is 12000 dm3Mol-1cm-1.

4. Calculate the molar absorptivity of a 1 x 10-4 M solution, which has an absorbance of 0.20, when
the path length is 2.5 cm.

5. The concentration of yeast t-RNA in an aqueous solution is 10 M. The absorbance is found to be

0.209 when this Solution is placed in a 1.00 cm cuvette and 258 nm radiations are passed through it.
a) Calculate the specific absorptivity, including units, of yeast t-RNA. b) What will be the
absorbance if the solution is 5 M? c) What will be the absorbance if the path length of the original
solution is increased to 5.00 cm?
 PROBLEMS
6. Calculate the molar absorptivity of a 0.5 x 10-3 M solution, which has an absorbance of 0.17,
when the path length is 1.3 cm.

7. A CaCO3 solution shows a transmittance of 90%, when taken in a cell of 1.9 cm thickness.
Calculate its concentration, if the molar absorption coefficient is 9000 dm3Mol-1cm-1.

8. Extinction coefficient of NADH at 340 nm is 6440 Lmol-1cm-1whereas NAD does not absorb at
340nm. What absorbance will be observed when light at 340 nm passes through a 1cm cuvette
containing 10uM NADH and 10 uM NAD.

9. A 1.00 × 10–4 M solution of an analyte is placed in a sample cell with a path length of 1.00 cm.
When measured at a wavelength of 350 nm, the solution’s absorbance is 0.139. What is the
analyte’s molar absorptivity at this wavelength?

10. The absorbance of a Cu sulphate solution containing 0.500 mg Cu/mL was reported as 0.3500 at
440 nm. a) Calculate the specific absorptivity, including units, of Cu sulphate on the assumption
that a 1.00 cm cuvette was used. b) What will be the absorbance if the solution is diluted to twice its
original volume?