Black body Radiation

History:

1. Until The end of 19^th century (Newtonian Mechanics).
2. 1905 Einstein special Relativity (C play a fundamental role),It does not modify distinction b/w matter & Radiation (referred as classical).
3. During the late 19^th century experimental evidence accumulated new concepts different from classical Mechanics. i.e Quantization of physical quantities energy & Angular momentum, The particle properties of radiation and the properties of matter. As velocity c plays a central role in relativity so does in planks constant in quantum mechanics .

Concept of Photon

Thomas Youngs's 1801 double slit experiment provides strong evidence that visible light is wave like. i.e all radiation in EMS have wave like aspect (X ray diffraction).

Another property of light is particle nature (Packet of energy E= hf) strongly supported by Photo Electric effect, compton effect etc.

Q: How photon was introduced?

• The concept of photon was introduced into physics by studies of the radiation emitted by heated objects In 1905 Einstein introduced the concept of photon while performing photo electric Effect.
• Most objects absorb light and emit Electromagnetic radiation when their temperatures are high.
• The radiations emitted by hot objects are called Thermal radiation.
• Such radiation is distributed continuously in wavelength, having measurable intensity throughout broad range of Electromagnetic spectrum.

In 19th century investigators discovered two important qualitative properties of thermal radiation

• As the temperature of the body increased, the intensity of the emitted radiation rises rapidly.
• The higher the temperature the shorter the wavelenght of emitted radiation.
• In order to attempt above two qualitative observations quantitatively was a difficulty i.e nature of emitted radiation, factors affecting intensity , temperature and body surface roughness etc. no fundamental law of physics seems to be lurking behind such asensitive experiment.
• The solution to this difficulty was proposed in 1859 when Kirchhoff consider cavity in solid body its wall at uniform temperature with a small hole in its wall.
• The radiation emerging from the hole should not depend on the material or the mode of construction of the cavity but depend only on temperature.
• Now stefan- Boltzmann constructed above ist qualitative statements quantitatively IM-- sT⁴ 1(T) represents the total radiated power integral over all wavelenghts.
• The second statement was expressed by wien's ImaxT = 2.898 x 10^-3 m * K
• max is the wavelenght at which the radiation emitted by a cavity at temperature T has its max intensity. As the increases body color shifts to smaller wavelenghts and it glows yellow orange. Wiens law can be used to deduce the surface temperature of stars from their color, blue stars being hotter than red stars.
• An early classical attempt to explain blackbody radiation was the Rayleigh-Jeans law
• At long wavelengths, the law matched experime At short wavelengths, there was a major disagreement between the Rayleigh-Jeans law and experiment.
• This mismatch became known as the ultraviolet catastrophe.
• You would have infinite energy as the wavelength approaches zero ntal results fairly well.
• In 1900 Planck developed a theory of blackbody radiation that leads to an equation for the intensity of the radiation.
• This equation is in complete agreement with experimental observations.
• He assumed the cavity radiation came from atomic oscillations in the cavity walls. Planck made two assumptions about the nature of the oscillators in the cavity walls
• The energy of an oscillator can have only certain discrete values E_n - E_n=nhf n is a positive integer called the quantum number f is the frequency of oscillation h is Planck's constant

-  This says the energy is quantized.

- Each discrete energy value corresponds to a different quantum state.

• Each quantum state is represented by the quantum number, n
• The oscillators emit or absorb energy when making a transition from one quantum state to another.
• The entire energy difference between the initial and final states in the transition is emitted or absorbed as a single quantum of radiation.
• An oscillator emits or absorbs enerav only when it changes auantum states.
• The radiation emerging from the hole should not depend on the material or the mode of construction of the cavity but depend only on temperature.
• Now stefan- Boltzmann constructed above ist qualitative statements quantitatively.
• 1(T)= sT⁴
• 1(T) represents the total radiated power integral over all wavelengths.
• The second statement was expressed by wien's ImaxT = 2.898 x 10^-3 m K _max is the wavelenght at which the radiation emitted by a cavity at temperature T has its max intensity. As the increases body color shifts to smaller wavelenghts and it glows yellow orange . Wiens law can be used to deduce the surface temperature of stars from their color, blue stars being hotter than red stars.
• An early classical attempt to explain blackbody radiation was the Rayleigh-Jeans law
• At long wavelengths, the law matched experime At short wavelengths, there was a major disagreement between the Rayleigh-Jeans law and experiment.
• This mismatch became known as the ultraviolet catastrophe.
• You would have infinite energy as the wavelength approaches zero ntal results fairly well.
• In 1900 Planck developed a theory of blackbody radiation that leads to an equation for the intensity of the radiation.
• This equation is in complete agreement with experimental observations.
• He assumed the cavity radiation came from atomic oscillations in the cavity walls. Planck made two assumptions about the nature of the oscillators in the cavity walls
• The energy of an oscillator can have only certain discrete values E_n - E_n=nhf n is a positive integer called the quantum number
• f is the frequency of oscillationh is Planck's constant

-  This says the energy is quantized.

-  Each discrete energy value corresponds to a different quantum state.

• Each quantum state is represented by the quantum number, n
• The oscillators emit or absorb energy when making a transition from one quantum state to another.
• The entire energy difference between the initial and final states in the transition is emitted or absorbed as a single quantum of radiation.
• An oscillator emits or absorbs energy only when it changes quantum states.
• The energy carried by the quantum of radiation is E = h f.

Academic Essay Writing

• Analyse the task - know what is expected, and who your audience is. The words of the question are very important: do you discuss, compare, explain etc. This is just as important if you are writing your own question (which you should address in the introduction).
• Research, research, research! Keep notes, and keep track of your references (and page numbers for direct quotations.)
• Plan your essay. Structure your points and know what you are going to say before you think about how you are going to say it.

Consider the best organisation of the essay - should it be broken into sections?

• Introduction, body and conclusion again follow the mantra of telling them what you will tell them, then telling them, then telling them what you have told them. The introduction should give a very brief background (one or two sentences), provide a short overview, state your view and state clearly what the outcome/main aim of the paper is. Each paragraph of the body should contain a main point for supporting the aim of your essay. The conclusion should summarise the main points and the overall view and response to the question or aim.
• It is important that your own voice/views come through (with arguments to support these views), and that it is not simply a regurgitation of information already existing in the literature. Evaluation of the essay will involve evaluating your attempt at independent critical thinking.
• Write in an appropriate style - use formal academic language.
• There are many different referencing styles, and you should always check what the required format is. In scientific writing it is common to use numbered references, listed either in order of reference or alphabetically. The title of the journal or book is almost always italicised, and the journal number is written in bold. The year of publication appears immediately after the author names. An example would be: [1] Einstein A, Podolsky B and Rosen N 1935 Can quantum-mechanical description of physical reality be considered complete. Phys. Rev. 47 777 It is essential that the format is consistent. If abbreviations are used (above we have abbreviated Physical Review) it is essential that the standard convention is adhered to.
• Only use "et al" if there are more than three authors (if you use a referencing software such as BibTeX this will automatically do the formatting for you when you select the appropriate style).
• Proof-read thoroughly.