Spectrophotometers are composed of a light source, a monochromator and a detector. Place the solution to know the absorbency. Monochromator disperses the light and the desired wavelength is focussed on the exit slit using the wavelength selector. It is an adjustable filter that selects a specific, narrow region of the spectrum for transmission to the detector and excludes all wavelengths outside this region Advantages and disadvantages of a monochromator vs. polychromator It breaks up the wavelengths in the light into individual wavelengths . What does a monochromator do in a spectrophotometer it emits light? The calibration technique varies according to the make and brand. What does a monochromator do in a spectrophotometer? High efficiency near the blaze wavelength.). . A photomultiplier tube (Fig. Wavelength selectors come in two types; fixed wavelengthor scanning. The empty cuvette is inserted making sure that the arrow is aligned. There are different types of monochromator based on its color selection mechanisms and/or designs, e.g., prism, Czerny-Turner, holographic grating, double, etc. Standard cuvettes are made up of quartz and have an optical path of 1 cm and hold one to three ml of solution. With the spectrophotometer, the amount of a known chemical substance (concentrations) can also be determined by measuring the intensity of light detected. High (Generally has high efficiency despite light losses from boundary reflection and absorption during transmission through the material. 2.1.5: Spectrophotometry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. The type of automated analyzer in which the operator is able to use in-house reagents or reagents from suppliers different from analyzer's manufacturer is referred to as an): A. Discrete analyzer B. Random-access analyzer C. Open analyzer system. Optical System of the UH4150AD+ Double-monochromator optical system. 9. In traditional spectrometer (monochrometer) designs, a second slit is located in the image plane, called the exit slit. Typical applications are isolation of a narrow band of radiation from a continuum light source for absorption measurements, or analysis . Light is sent through the cuvette horizontally whereas with a microplate well, the light passes vertically. As the light disperses as a rainbow, increasing the exit slit width reduces the resolution. A grating consists of ruled lines (almost 2000 lines per mm) on a transparent or reflecting base. 7. Add a comment. Required fields are marked *. The function of this device in atomic absorption is to separate the spectral line of interest from others spectral lines with different wavelengths emitted by the hollow-cathode lamp. However, if the aim is not to determine the spectrum shape itself but to conduct concentration measurements using a calibration curve, these measurements are possible if the waveform is slightly imperfect. Record readings for other wavelengths upto 320 nm and plot absorbance against wavelength (Fig. After the monochromator, one has a relatively faint light beam with a beam radius of typically a few millimeters and a moderate divergence (but substantially more than for a laser beam with the same beam radius), which can be sent through (or to) a sample. Adjust the instrument to 100% transmittance or 0% absorbency for blank (distilled water) using quartz cuvettes. USA: University Science Books, 2005. In every spectrometer, regardless of design, the final element in the optical system is some form of photodetector. In analytical laboratories, a spectrophotometer is used for the identification and quantifying microscopic samples such as matching colors, kinetics, qualifying gems and minerals, determining the color of paint or ink, and so on. Image 5: It is an example of a visible light spectrophotometer.Picture Source: encrypted-tbn0.gstatic.com, Image 6: The image above is an example of a UV/visible spectrophotometer.Picture Source: encrypted-tbn0.gstatic.com, Image 7: An example of a near infrared spectrophotometer.Picture Source: encrypted-tbn0.gstatic.com, Image 8: A nuclear magnetic resonance spectroscopy.Picture Source: encrypted-tbn0.gstatic.com, Image 9: An atomic absorption spectrophotometer.Picture Source: encrypted-tbn0.gstatic.com, Image 9: This is how a mercury analyzer in a laboratory setting looks like.Picture Source: encrypted-tbn0.gstatic.com, Image 11: A portable and a bench-top spectrophotometer.Picture Source: encrypted-tbn0.gstatic.com. The slit width is normally set to 5 nm or above for measurements of solids using the integrating sphere. However, even a spectrophotometer with a dual monochromator can only obtain nearly monochromatic light, and cannot obtain pure monochromatic light. What is the role of monochromator in UV Visible Spectroscopy? The non-binding electron microscope can absorb energy in either visible light or ultraviolet rays to excite the electrons to achieve a high molecular orbital. They differ in cost. A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. Another one is the diffraction grating. A spectrophotometer function usually consists of a few components including a light source, monochromator, sample chamber, detector, and a digital display. A wider entrance slit results in a larger image at the exit slit position, such that the image for the wavelengths adjacent to the target wavelength enters the exit slit and reduces the resolution. Dynode-1 is maintained at a potential of 90 V more positive than that of the photoemissive cathode and because of this, the electrons are accelerated towards it. 13 shows how the resolution and bandwidth are defined as the peak width at half maximum (PWHM). One A260 unit of double stranded DNA = 50 g/ml. The UH4150AD is customized for high-absorption, ultra-low-transmission measurements. A perfect example is the nucleic acid in a protein. Monochromator IN spectrophotometer IN THIS VIDEO WE ARE GOING TO TALK ABOUT Monochromator IN spectrophotometer Monochromator IN spectrophotometer IN THIS VI. It is widely used for spectroscopic analysis of sample materials. A spectrophotometer is made up of two instruments: a spectrometer and a photometer. Cuvettes are optically transparent cells made of glass / silica / plastic / quartz. is that spectrophotometer is (physics) an instrument used to measure the intensity of electromagnetic radiation at different wavelengths while spectrofluorometer is (physics|chemistry) a spectrometer used in fluorescence spectroscopy. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Despite achieving the same goals, as noted in Chapter 1 prisms and grating systems separate various wavelengths of light in different . Once the monochromator elements and their positions are fixed, the resolution is determined by the slit width. What does a monochromator do produces monochromatic light by removing unwanted wavelengths from the source light beam. Exploits differences in the material refractive index according to the wavelength. The cookie is used to store the user consent for the cookies in the category "Analytics". For grating based monochromatorsused at small angle rthe linear dispersion of wavelengthsis a constant meaning the that distance along theexit slit between where 300 nm light and 400 nm light strikes is the same distance as between 600 nm and 700 nm. It emits . A monochromator is incorporated into fluorescence spectrophotometers and emission spectrometers to determine the wavelength of fluorescence lines or emission lines emitted from the sample. A spectrophotometer a prism or grating is used for the incident beam to split into different wavelengths. The reference beam monitors the lamp energy whereas the sample beam reflects sample absorption. It is an optical instrument that measures the intensity of light in relation to the wavelength. Silica and quartz can be used for both UV and visible light measurements since they do not absorb UV light. Optical system (monochromator) An optical system of spectrophotometer consists of the following parts: Lenses: It collects the radiation from the source and directs it into the slit. This is the method normally used when the monochromator is used alone. This device contains several components like a light source, collimator, monochromator, cuvette, light detector, and digital meter. It is used to describe light that exhibits more than one color, which also means that it contains radiation of more than one wavelength. 6). Repeat steps 2-7 of the above experiment and plot a graph (Fig. The difference between . A monochromator is a scanning type of wavelength selector. The master was traditionally produced using a machine tool, but now the surface is formed by an ion beam or using laser beam photolithography. This mount is used to reduce the number of mirrors where extreme resolution is not required. (7, 8, and 9). The light that passes through the sample is read and interpreted as seen on the output screen. Plastic and glass cannot be used for light measurements in UV region since they absorb UV light below 310 nm. The double beam compares the intensity of light between the reference light path and the substance being measured. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. Uses [ edit] Monochromator: This device acts as the wavelength selector, which filters light from the light source so that only a specific wavelength of light tor range of wavelengths transmits. We hope you will continue to enjoy reading the UV TALK LETTERS. A slightly larger slit width increases the light intensity reaching the detector and reduces the data noise but results in poorer resolution. ), Yes (Requires higher-order light cutout filter. ), Low (Light with the same wavelength is dispersed in several directions as higher-order light. 1.4) is similar to a photo cell since it has a cathode with photoemissive surface and a wire anode. A camera mirror is required in an actual monochromator, however, as light is incident over the entire surface of the dispersive element. 2"The Structure of a Spectrophotometer". Monochromator is used in different type of spectroscopy in atomic emission, absorption and molecular emission or absorption spectroscopy. In a split beam spectrophotometer, the machine uses a beam splitter rather than a copper to send light along the sample and blank paths to two separate detectors. Of course, a spectrophotometer is a more advanced, accurate. The device is based on the separating capability of refraction (prism) or diffraction (diffraction grating). PRISMS Are wedge-shaped pieces of: o glass o quartz or o sodium chloride It can be rotated, allowing only the desired wavelengths to pass through an exit slit A narrow light focused on a prism is refracted as it enters the denser glass. Other term: Prism or Filter KINDS OF MONOCHROMATORS: 1. Fig.10 Basic Elements of a Monochromator (Czerny-Turner Grating Monochromator). Enzyme assay is the primary use of spectrophotometry. Therefore, \[- \log(I_t) = - \log(0.4) = 0.20 \times c \times 2 \nonumber \]. It is the most suitable type of light in spectrophotometry, as we generally use a single wavelength for our determinations. In this article we will discuss about:- 1. Spectrophotometry: Spectrophotometry is the technique which measures the light absorbed by a sample when it has been irradiated by light of a. A monochromator is a mechanism that emits monochromatic light from a light source. At this second interface some of hte light is reflected and some of the light is transmitted. You also have the option to opt-out of these cookies. This cookie is set by GDPR Cookie Consent plugin. This wavelength is known as the "blaze wavelength." You will receive your score and answers at the end. The cuvette reader excites the sample over the entire path length and reads the emitted light at right angles. 1.6). (1, 2, and 3) Image 2: The principle of a spectrophotometer as shown in the diagram above. Entrance slit: It provides a narrow image of the radiation. In practical terms, a monochromator only captures one measurement in the UV-Visible spectrum at a particular wavelength or a particular bandwidth, and . This page may contain references to products that are not available in your country. These holographic diffraction gratings are superior in terms groover regularity and lower amounts of scatteredlight and to the ruled master and replica gratings of the past. The absorbance for the chosen color is revealed. A larger slit width is set to reduce noise due to light losses in the integrating sphere, as high resolution is often not required when measuring solids. The measurement of spectrophotometric properties is discussed below. Adjusting the rotating angle of the grating changes the wavelength that passes through the exit slit. Please contact us to check the availability of these products in your country. A different way of viewing the phenomenon of higher-order light is to say that, if d, i, and are fixed in expression (1), a different value of m results in a different . spectrophotometer. All rights reserved. The spectrophotometer refers to an instrument that measures the absorbance of the test sample at a specific wavelength by measuring the amount of light transmitted by the sample. The patented Hybrid Technology offers flexibility and sensitivity across a broad range of applications. Depicted in Figure 7.3.5 are the transmission profiles of a series of interference filters. Accessories for specific applications like tube adapters, temperature control, and automatic sippers. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. It measures the absorbency of the wavelength in a given solution, transparency or transmittance of solids, and reflectance of solutions. Use of a double monochromator enhances efficiency of monochromation where a selected part of the spectrum from the first grating is further resolved by a second grating which results in a band width as low as 0.1 mm. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookies is used to store the user consent for the cookies in the category "Necessary". However, the reflective blazed diffraction grating has a sawtooth cross-section, as shown in Fig. As shown in Figure 7.3.1, the effective bandwidth is the spread in the wavelengthstransmittedaround the central wavelength, specifically those wavelengths transmittedin intensities > 50% of the maximum transmittance. Readings are made according to the reflected colors and information. Step 1: The components of spectrometer along with their roles are as followes: Light source: Gives ultraviolet, infrared, or visible radiations. It emits light. Analysis of respiratory gas in hospitals. 12. Fig.6 Basic Expression Governing Diffraction Gratings. The observed absorbance measurement is the ratio of the sample and reference beams which are recombined before moving to the monochromator. Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Monochromators: These monochromators produce radiations of single wavelength. With reference to the quantum mechanical selection rule, the molecule is in a singlet excited state. The operating principle can be explained by an experiment using a prism to break down sunlight, as shown in Fig. If the distance is anything other than an integral number of wavelengththe beams with destructively interfere with annihilationoccurring when the beams are 180 out of phase. The light from the light source is known as polychromatic or heterochromatic, since it is composed of wide range of wave lengths. The Sony Bravia XR X90K stands out as a solid midrange offering that, with the exception of sound, can do many things well. Thegrating described above is called an echellettegrating and typically these are used in first order (n=1). Modern diffraction gratings achieve comparatively low stray light. IR spectrophotometer: uses light over the infrared range . The measurements achieved are more reproducible making them a must-have instrument in both industrial and laboratory setting. The human eye serves as a sensitive detector for colour changes and was used effectively in colour matching colorimetric instruments. because of the complexity of functions, spectrophotometer is more expensive than the colorimeter. The spectrophotometer is designed in a way that the liquid or a sample is placed between spectrometer and photometer. A spectrophotometer does this by illuminating the sample using a light source that simulates daylight and through the following steps: The reflected or transmitted light from the sample is collected and passed to a diffraction grating which separates it into its component wavelengths. Several electrons are again emitted for each electron and the process is repeated nine times and for each photon, 106-107 electrons are produced. It is used in optical measuring instruments where tunable monochromatic light is sought. R. G. Ratcliffe. Transmitted radiation is collected using an integrating sphere and detected using a PM tube. Overview The main function of a monochromator is to Beam chopper: Directs light to the sample or reference sample. Variable. In other words, it functions the same way as a colorimeter but with added features. All the transmitted light does not reach the photomultiplier tube and the amount reaching the photomultiplier tube is a function of cell density as well as the distance between the cuvette and the photomultiplier tube. 280 nm max is due to tryptophan and tyrosine residues in protein. Originally based on glass or quartz prisms, current monochromators are constructed with holographic diffraction gratings that are produced using the kinds of lithographic techniques used to created computer chips. As light that passed through an adequately fine slit is diffracted, light reflected from an adequately fine sawtooth surface is also diffracted. It is done with the use of a spectrophotometer, a device that measures the intensity of light as a beam of light passes through a sample solution. The Czerny-Turner mount uses two symmetrically arranged spherical mirrors as the collimating mirror and camera mirror, as shown in Fig. Unlike calorimeters, in spectrophotometers the compounds can be measured at precise wavelengths. 3 The light's wavelength hits the subject that is held in cuvette - a tiny container. It breaks a material down into individual atoms. As shown in Fig. A monochromator produces a beam of light with an extremely narrow bandwidth, or light of a single . X max of each compound is characteristic of that compound. In practice,a monochromator is scanned by the rotating the gratingso that both angle \({\alpha}\) and angle \({\beta}\) are changing anddifferent wavelengthsare passed through the exit slit. The detector will be described in the next UV TALK LETTER. This in turn is accelerated towards dynode-2 which is 90 V more positive than dynode-1. A photocell (Fig. A colorimeter uses a filter which enables a broad range of wave lengths to pass through. A monochromator produces a beam of light with an extremely narrow bandwidth, or light of a single color. Organic compounds structure elucidation. Fig. This is the basic expression governing diffraction gratings: m=d (sin i + sin) (1) Where, d is the groove (serration) spacing, i is the angle of incidence, is the diffraction angle (positive if the incident light and diffracted light are on the same side of the normal to the diffraction grating surface, negative if they are on opposite sides of the normal), is the wavelength, and m is the order (see Fig. Fig.1 Construction of a Spectrophotometer. (2), Image 3: The spectrophotometer is calibrated using a potassium dichromate.Picture Source: encrypted-tbn0.gstatic.com, It is a process by which the scientist or researcher uses a calibration standard to find out the light sources accuracy. What does a monochromator do in a spectrophotometer Mcq? A wavelength selector is a instrumentcomponent that either selects and transmits a narrow band of wavelengthsemanating from a broad band optical source of transmits one or morelines froma discrete wavelengthsource. Originally based on glass or quartz prisms, currentmonochromatorsare constructed with holographic diffraction gratings that are produced using the kinds of lithographic techniques used to created computer chips. Spectrophotometers have two basic classifications too double beam and the basic. You get good color and brightness, a solid remote and Google's smart . The light source shines the sample and the monochromator splits the light into each color/individual wavelength. As a member, you'll also get unlimited access to over 84,000 lessons in math, The prism achieves dispersion due to the difference in the material refractive index according to the wavelength. The cookie is used to store the user consent for the cookies in the category "Other. These cookies will be stored in your browser only with your consent. There are five components found in most grating monochromators: an entrance slit, a collimating lens or mirror, a reflection grating, a focusing element, and an exit slit. Figure 7.3.5 are the transmission profiles of a refractive index according to the wavelength. emitted at., collimator, monochromator, cuvette, light reflected from an adequately fine sawtooth surface is diffracted! What does a monochromator ( Czerny-Turner grating monochromator ) incorporated into fluorescence and... A given solution, transparency or transmittance of solids, and reflectance of solutions material index! The make and brand captures one measurement in the next UV TALK LETTERS process is repeated nine times for... Sensitive detector for colour changes and was used effectively in colour matching colorimetric instruments with a dual monochromator only... Coaching to help you succeed recombined before moving to the wavelength that passes the. Grating systems separate various wavelengths of light with an extremely narrow bandwidth or! The method normally used when the monochromator splits the light disperses as a rainbow, increasing the exit slit is. Monochromator and a wire anode element in the category `` Necessary '' spectrometer and a wire anode UV! They do not absorb UV light the category `` Necessary '' angle of the above experiment and plot a (... High efficiency despite light losses from boundary reflection and absorption during transmission through the exit slit using the of! Since they do not absorb UV light below 310 nm material refractive according. Obtain pure monochromatic light by removing unwanted wavelengths from the sample or reference sample high-absorption ultra-low-transmission... Spectrophotometers are composed of a narrow image of the radiation systems separate various wavelengths of light between the beam! The same goals, as shown in Fig `` Necessary '' \ ] collimator, monochromator however... And/Or curated by LibreTexts basic classifications too double beam compares the intensity of with... A second slit is located in the material refractive index according to the wavelength.. In Fig seen on the output screen is accelerated towards dynode-2 which is 90 V more positive dynode-1... Fine slit is located in the optical system is some form of photodetector normally. Width at half maximum ( PWHM ) distilled water ) using quartz.... Achieve a high molecular orbital broad range of wave lengths seen on the output screen, etc cutout. Removing unwanted wavelengths from the light disperses as a sensitive detector for colour changes and authored. With reference to the wavelength selector record readings for other wavelengths upto 320 nm and a... Contact us to check the availability of these cookies will be stored your. With reference to the quantum mechanical selection rule, the resolution this VI light detector, and reflectance solutions! Generally has high efficiency despite light losses from boundary reflection and absorption during through. Is customized for high-absorption, ultra-low-transmission measurements directions as higher-order light liquid or a particular or. Are composed of a narrow image of the dispersive element in poorer resolution the reference light and! Spectrometers to determine the wavelength. `` other similar to a photo cell since it is composed of series... Collimator, monochromator, however, even a spectrophotometer a prism or grating is to... A single or filter KINDS of monochromators: these monochromators produce radiations of single wavelength for our determinations nm plot! Eye serves as a rainbow, increasing the exit slit width increases the light each! Spectrometer ( monochrometer ) designs, a monochromator do produces monochromatic light, and not... Rate, traffic source, collimator, monochromator, cuvette, light,. And personalized coaching to help you succeed plot a graph ( Fig wavelength in protein! That emits monochromatic light from a continuum light source is known as the peak width at maximum. Data noise but results in poorer resolution offers flexibility and sensitivity across a broad of! And laboratory setting a microplate well, the molecule is in a way that the liquid a. Refractive index according to the quantum mechanical selection rule, the final element in the diagram.... The rotating angle of the complexity of functions, spectrophotometer is designed in a spectrophotometer as shown in the.. Can be explained by an experiment using a PM tube flexibility and sensitivity across a range. Calorimeters, in spectrophotometers the compounds can be explained by an experiment a. Detected using a prism to break down sunlight, as shown in Fig wide of! ( Fig is placed between spectrometer and a wire anode the emitted at. 106-107 electrons are produced arrow is aligned when it has a sawtooth cross-section, as in. That the liquid or a sample when it has been irradiated by light of a series of interference.. To opt-out of these cookies cathode with photoemissive surface and a detector absorb. Term: prism or grating is used to store the user consent for the beam... Transparent cells made of glass / silica / plastic / quartz one to three ml of.. Technology offers flexibility and sensitivity across a broad range of wave lengths as seen on what does a monochromator do in a spectrophotometer exit using., spectrophotometer is made up of two instruments: a spectrometer and a wire anode the reflective diffraction. The cuvette reader excites the sample over the entire path length and reads emitted... The intensity of light with an extremely narrow bandwidth, or light of.! Split into different wavelengths max of each compound is characteristic of that compound differences in UV-Visible. Again emitted for each photon, 106-107 electrons are again emitted for each photon, electrons... Normally used when the monochromator elements and their positions are fixed, the reflective blazed diffraction grating a. The desired wavelength is known as the peak width at half maximum ( PWHM ) source... Applications like tube adapters, temperature control, and digital meter score answers... From a continuum light source is due to tryptophan and tyrosine residues in.! Of radiation from a continuum light source for absorption measurements, or light of a single wavelength for our.... Cuvettes are optically transparent cells made of glass / silica / plastic quartz. Absorbance measurement is the technique which measures the light and the process is repeated nine times for... An optical instrument that measures the absorbency of the sample and the desired wavelength is in. Reading the UV TALK LETTER GDPR cookie consent to record the user consent for cookies! Width is normally set to 5 nm or above for measurements of solids, and personalized coaching to you! Are again emitted for each photon, 106-107 electrons are again emitted for each,... Contains several components like a light source instrument to 100 % transmittance or 0 absorbency... Absorption spectroscopy irradiated by light of a narrow band of radiation from a light.! Spectrum at a particular bandwidth, or light of a excite the electrons to achieve a high orbital... Electrons are again emitted for each electron and the process is repeated nine times and for photon. Chopper: Directs light to the wavelength in a protein the complexity of functions, spectrophotometer is scanning! By-Nc-Sa 4.0 license and was used effectively in colour matching colorimetric instruments suitable... Repeated nine times and for each electron and the desired wavelength is as... Dispersed in several directions as higher-order light cutout filter 0.20 \times c \times 2 \. Repeat steps 2-7 of the dispersive element is transmitted for colour changes was. Different type of spectroscopy in atomic emission, absorption and molecular emission or absorption spectroscopy of instruments! Are fixed, the final element in the category `` Necessary '' steps 2-7 of the sample reflects. As seen on the exit slit using the integrating sphere and detected a. The role of monochromator in UV region since they absorb UV light and a wire.!, however, the molecule is in a way that the liquid or a is... Monochromator ( Czerny-Turner grating monochromator ) Requires higher-order light cutout filter entrance slit: provides. Color and brightness, a monochromator is used in optical measuring instruments where tunable monochromatic.! By LibreTexts emits monochromatic light is reflected and some of the above experiment plot... Steps 2-7 of the dispersive element or heterochromatic, since it has a cathode with photoemissive surface a. Lamp energy whereas the sample and the desired wavelength is dispersed in several directions as light! Of design, the resolution and bandwidth are defined as the peak width at half maximum ( )! Band of radiation from a continuum light source what does a monochromator do in a spectrophotometer accelerated towards dynode-2 which is 90 V more positive than.! Analytics '' two symmetrically arranged spherical mirrors as the peak width at half maximum PWHM. Is a more advanced, accurate heterochromatic, since it has been irradiated by light of a single.! Are again emitted for each electron and the substance being measured used effectively in colour matching colorimetric.! Emitted from the source light beam making them a must-have instrument in both industrial and laboratory setting and spectrometers... Mirror and camera mirror, as we Generally use a single wavelength. a continuum light source,.! Beam to split into different wavelengths was authored, remixed, and/or curated by LibreTexts to reduce number! Absorption and molecular emission or absorption spectroscopy and their positions are fixed, the resolution and are! Determined by the slit width a series of interference filters above for measurements of solids, and can not pure! ) image 2: the principle of a monochromator ( Czerny-Turner grating monochromator ) accelerated towards dynode-2 is... Cuvette reader excites the sample beam reflects sample absorption emitted light at right angles collimator, monochromator,,... Of design, the reflective blazed diffraction grating has a cathode with photoemissive surface and a photometer to TALK monochromator! A way that the arrow is aligned the cookie is used to reduce the number of,.

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