Chapter 18: Example Unit Conversions with Light | CHM 214 | 152

Jacob Stewart
16 Apr 202104:51
EducationalLearning
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TLDRThe video script discusses the properties of light, focusing on infrared spectroscopy to analyze functional groups in organic molecules. It illustrates how to calculate the wavelength, frequency, and energy (in joules per photon) of light at 3000 wave numbers, using the principles of wave properties and Planck's constant. The example demonstrates the conversion between different light properties and emphasizes the relatively low energy of a single photon compared to macroscopic scales.

Takeaways
  • 🌟 Infrared spectroscopy is used to analyze functional groups in organic molecules, particularly the CH stretch region.
  • 📐 The absorption of CH single bonds occurs at approximately 3,000 wave numbers.
  • 🔄 Wave number (cm⁻¹) can be converted to wavelength (cm) using the formula λ = 1/wave number.
  • 📏 Wavelength is typically expressed in micrometers for infrared spectroscopy, with 3.33 μm corresponding to a 3,000 cm⁻¹ wave number.
  • 🌐 The speed of light (c) is 2.998 x 10⁸ m/s, and can be used to calculate frequency (ν) using the equation ν = c/λ.
  • 🖥️ When calculating frequency, it's important to ensure unit consistency, such as converting meters to centimeters if needed.
  • 🎢 The frequency of light corresponding to a 3,000 cm⁻¹ wave number is 8.99 x 10¹³ Hz.
  • 💡 Planck's constant (h) is 6.626 x 10⁻³⁴ Js and is used to calculate the energy (E) of a photon using the equation E = hν.
  • 🌠 A single photon at 3,000 cm⁻¹ wave number has an energy of 5.96 x 10⁻²⁰ J, which is relatively low compared to macroscopic energy levels.
  • 🔍 The process of converting between wavelength, frequency, wave number, and energy per photon is essential for understanding the properties of light.
  • 🚀 This example illustrates the application of fundamental physics concepts in the study of light and its interaction with matter.
Q & A

  • What is the topic of discussion in the transcript?

    -The topic of discussion is the properties of light, specifically focusing on an example calculation related to infrared spectroscopy and its application in identifying functional groups in organic molecules.

  • What is the significance of the CH stretch region in infrared spectroscopy?

    -The CH stretch region is significant in infrared spectroscopy because it helps identify the presence of CH single bonds in organic molecules. An absorption at about 3000 wave numbers is indicative of this.

  • How is the wavelength related to the wave number?

    -The wavelength is inversely related to the wave number. The wavelength can be calculated as one over the wave number, which gives the distance between the peaks of the wave.

  • What is the calculated wavelength for a 3000 wave number absorption?

    -The calculated wavelength for a 3000 wave number absorption is 3.33 micrometers, after converting from centimeters to micrometers.

  • How can we find the frequency of light corresponding to a given wave number?

    -The frequency of light can be found using the equation nu (frequency) equals c (speed of light) over lambda (wavelength) or c times the wave number. For the given wave number of 3000 cm^-1, the frequency is 8.99 x 10^13 Hz.

  • What is the energy of a single photon corresponding to a 3000 wave number absorption?

    -The energy of a single photon corresponding to a 3000 wave number absorption is 5.96 x 10^-20 Joules. This is calculated using Planck's constant (h) times the frequency (nu).

  • How does the energy of a single photon of infrared light compare to that of visible light?

    -The energy of a single photon of infrared light (around 10^-20 Joules) is less than that of visible light, which is around 10^-19 Joules. This difference reflects the fact that infrared light has a longer wavelength and lower frequency than visible light.

  • Why is it difficult to express the energy of a photon in joules per photon?

    -It is difficult to express the energy of a photon in joules per photon because the values are very small, making them cumbersome to work with. Therefore, other units are often used to express these energies.

  • What is the importance of understanding the relationship between wavelength, frequency, and energy in the context of spectroscopy?

    -Understanding the relationship between wavelength, frequency, and energy is crucial in spectroscopy as it allows scientists to identify and analyze the molecular structures of substances by correlating their absorption or emission spectra with these properties of light.

  • How does the example calculation in the transcript demonstrate the wave-particle duality of light?

    -The example calculation shows the wave-particle duality of light by discussing both the wave properties (wavelength and frequency) and the particle properties (energy per photon). It illustrates how these different aspects of light can be calculated and related to each other.

  • What is Planck's constant and how is it used in the context of the calculation?

    -Planck's constant is a fundamental constant in quantum mechanics, denoted by 'h', with a value of 6.626 x 10^-34 Js. It is used in the calculation to convert the frequency of light into its corresponding energy per photon using the equation E = h * nu.

Outlines
00:00
🔬 Infrared Spectroscopy and Organic Molecules

This paragraph discusses the application of infrared spectroscopy in analyzing functional groups within organic molecules. The focus is on the CH stretch region, which is indicative of CH single bonds. The absorption at approximately 3000 wave numbers is highlighted, and the process of converting this value to wavelength, frequency, and energy per photon is explained. The example demonstrates how to calculate the wavelength from wave numbers, determine the frequency using the speed of light, and find the energy of a single photon using Planck's constant. The comparison of the calculated energy with that of visible light provides context for the significance of these values in the study of light properties.

Mindmap
Keywords
💡Infrared Spectroscopy
Infrared spectroscopy is an analytical technique used to identify functional groups within organic molecules by examining the absorption of infrared light. In the context of the video, it is used to observe the CH stretch region, which helps in identifying the presence of CH single bonds in a molecule. The process involves measuring the absorption at about 3000 wave numbers, which corresponds to a specific wavelength and frequency of light.
💡Wave Number
Wave number is a dimensionless quantity that relates to the frequency of a wave and is often used in spectroscopy to describe the position of spectral lines. It is defined as the number of waves per unit length and is inversely proportional to the wavelength. In the video, the wave number of 3000 is used to identify the presence of a specific molecular vibration, and its conversion to wavelength and frequency helps in understanding the properties of the absorbed light.
💡Wavelength
Wavelength is the distance between two consecutive points in a wave that are in the same phase, such as two crests or two troughs. It is a fundamental property of light that determines the energy and frequency of a photon. In the video, the wavelength corresponding to the 3000 wave number absorption is calculated to be 3.33 micrometers, which is in the infrared region of the electromagnetic spectrum. Understanding the wavelength is crucial for identifying the type of molecular vibrations and the energy associated with the absorbed light.
💡Frequency
Frequency refers to the number of cycles a wave completes in a unit of time, typically measured in Hertz (Hz). It is closely related to the energy of a photon, with higher frequencies corresponding to higher energies. In the context of the video, the frequency of the light corresponding to the 3000 wave number is calculated using the speed of light and the wavelength, resulting in a frequency of 8.99 x 10^13 Hz. This frequency value is essential for understanding the energy of the absorbed light and its interaction with the molecules.
💡Photon
A photon is a quantum of electromagnetic radiation, representing the basic unit of light. It possesses both wave-like and particle-like properties, with its energy being directly proportional to its frequency. In the video, the energy of a single photon corresponding to the 3000 wave number absorption is calculated to be 5.96 x 10^-20 Joules. Understanding the energy of photons is crucial for studying the interactions between light and matter, as well as for applications in spectroscopy and quantum mechanics.
💡Planck's Constant
Planck's constant is a fundamental constant in quantum mechanics, denoted by the symbol 'h'. It relates the energy of a photon to its frequency, expressed by the equation E = hν (where E is energy, h is Planck's constant, and ν is frequency). In the video, Planck's constant is used to calculate the energy of a single photon, demonstrating its importance in understanding the quantum nature of light and its interactions with matter.
💡CH Stretch Region
The CH stretch region refers to a specific range of wave numbers or wavelengths in an infrared spectrum where the absorption of light is due to the vibrational stretching motion of carbon-hydrogen (CH) bonds. This is a characteristic feature in the infrared spectroscopy of organic molecules and helps identify the presence of CH single bonds. In the video, the absorption at about 3000 wave numbers is indicative of the CH stretch region, which is a key piece of information for analyzing the molecular structure.
💡Organic Molecules
Organic molecules are compounds containing carbon atoms covalently bonded to hydrogen, often with other elements such as oxygen, nitrogen, or sulfur. They form the basis of all living organisms and are the focus of study in organic chemistry and biochemistry. In the video, the properties of light are used to analyze functional groups within organic molecules, specifically by examining the CH stretch region through infrared spectroscopy.
💡Energy
Energy, in the context of physics and chemistry, refers to the capacity to do work or cause change. It is a fundamental concept that can exist in various forms, including kinetic, potential, thermal, and electromagnetic. In the video, the energy of a photon is calculated to understand the interaction between light and organic molecules. The energy per photon is a measure of the light's capacity to induce changes in the molecular structure or electronic states.
💡Functional Groups
Functional groups are specific arrangements of atoms within organic molecules that determine their chemical properties and reactivity. They are the building blocks of organic chemistry and are responsible for the characteristic reactions of different types of compounds. In the video, the use of infrared spectroscopy to identify functional groups, such as CH single bonds, is discussed as a way to understand the molecular structure and properties of organic molecules.
💡Light
Light is a form of electromagnetic radiation that is visible to the human eye and has both wave-like and particle-like properties. It can be characterized by its wavelength, frequency, and energy, all of which are interconnected. In the video, the properties of light are explored through the examination of its infrared spectrum, specifically focusing on how these properties relate to the structure and function of organic molecules.
Highlights

The discussion focuses on properties of light and its applications in infrared spectroscopy. (Start Time: 0s)

Infrared spectroscopy is used to analyze functional groups within organic molecules. (Start Time: 10s)

The CH stretch region is commonly examined in infrared spectroscopy. (Start Time: 20s)

Absorption at around 3,000 wave numbers is indicative of CH single bonds. (Start Time: 30s)

The example calculation involves converting wave numbers to wavelength, frequency, and energy per photon. (Start Time: 40s)

Wave number is defined as one over the wavelength. (Start Time: 50s)

The wavelength corresponding to 3,000 wave numbers is calculated to be 3.33 micrometers. (Start Time: 1m)

Frequency is determined by the equation c equals lambda times nu, where c is the speed of light. (Start Time: 1m 30s)

Frequency is calculated to be 8.99 x 10^13 cycles per second (hertz) for the 3,000 wave number CH stretch. (Start Time: 2m)

The energy per photon is found using Planck's constant multiplied by the frequency. (Start Time: 2m 30s)

The calculated energy per photon for the 3,000 wave number CH stretch is 5.96 x 10^-20 joules. (Start Time: 3m)

The example illustrates the conversion between different representations of light properties. (Start Time: 3m 30s)

The energy content per photon is small when compared to macroscopic scales. (Start Time: 4m)

Visible light has an energy of approximately 10^-19 joules per photon. (Start Time: 4m 30s)

The method allows for understanding the energy in a single photon, despite its small magnitude. (Start Time: 4m 45s)

The process demonstrates the interconnectivity of wavelength, frequency, and energy in the context of light. (Start Time: 5m)

Transcripts

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Infrared SpectroscopyPhoton EnergyWavelength CalculationFrequency AnalysisOrganic MoleculesCH StretchLight PropertiesQuantum MechanicsScience EducationPhoton Behavior