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Blackbody Radiation: Derivation of Planck’s Law Step-by-Step | CSIR-NET, GATE

Planck Blackbody Radiation Formula The spectral energy density of blackbody radiation as a function of frequency is given by Planck's radiation law: \[ u(\nu)d\nu = \frac{8\pi h\nu^3}{c^3} \frac{1}{e^{h\nu/kT}-1} \, d\nu \] where \(h = 6.626 \times 10^{-34} \, \text{J·s}\) is Planck's constant \(u(\nu)\) is the energy density of radiation per unit frequency interval \(\nu\) is the frequency \(T\) is the temperature \(k\) is the Boltzmann constant In these notes we will derive the above formula in a step by step manner. Waves in a Box Consider an electromagnetic wave travelling with the speed of light in some arbitrary direction represented by the position coordinate \(x\). If the wavelength of the wave is \(\lambda\), the amplitude of the wave along the \(x\)-direction can be written as \[ A(x) = A_0 \sin \left(\frac{2\pi x}{\lambda}\right) \] This expression can also be written in terms of the wave number \(k\): \[ A(x) = A_0 \sin(kx) \] where the ...

Nikola Tesla: Engineer and Inventor

The man who invented the 20th century is none other than Nikola Tesla. He is serbian-american inventor, electrical engineer, mechanical engineer and a futurist. Best known for Alternating current(AC) and electrical supply system. Nikola tesla Born - 10 July, 1856. Died - 7 January, 1943 (83 years). Beginning with a quote of Nikola Tesla- " The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane. " Eidetic Memory Tesla read many works. He can memorize complete books. He supposedly possessed a photographic memory. He was a polyglot, speaking eight languages: Serbo-Croatian, Czech, English, French, German, Hungarian, Italian, and Latin. Tesla related in his autobiography that he experienced detailed moments of inspiration. He often see blinding flashes of light before his eyes, also accompanied by visions. Many times the visions were related to the word or the idea that he was currently...

Production , Properties and Uses Of X-Rays

X-Rays Introduction X rays discovered by William Roentgen in 1895 honoured by Nobel Prize in 1901. Basically are high energy photons (1- 100Kev) or electro-magnetic radiation, having a very short wavelength of the order of 1A⁰. Typical x-ray wavelength lies between the range of 1 A⁰ and 100A⁰. Accordingly they are classified into hard X-rays and soft X-rays. Uses of X rays are multifold. Usually they are used in surgery, radiotherapy, engineering, industry, detective department, scientific research and so many other areas. Hence, the name X-rays is popularly known even to a common man. Production Of X-RAYS The modern X-ray tube was designed by Dr.Coolidge and is known after his name as coolidge tube. It is widely used for commercial and medical purposes. Construction and working of Coolidge Tube The construction of coolidge tube to produce X-rays is schematically shown below. The cathode C consists of a tungsten filament heated by p...

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