Month: February 2011

Introduction & Statement of Poincaré Conjecture

In 1904, the french Mathematician Henri Poincaré posed an epoch-making question in one of his papers, which asked:

If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere?

Cosmic Rays or Cosmic Radiation

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Soon after 1900 it was shown by scientists that the air in an ionisation chamber, which was completely protected against penetration of α , β and γ rays, by surrounding it with thick lead walls, was still conductive; and it was thought that the inns causing this conductivity were produced by some rays coming from an unknown source. Read More

Rayleigh- Jean’s Law

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Lord Rayleigh on classical limes made an attempt to explain the energy distribution in black body radiation, which was completed by Jeans in 1900. The result obtained by then is known as Rayleigh – Jean’s Law.

Black body emits radiation of continuously variable wavelength right from zero to infinity. This radiation can be imagined as broken up into monochromatic waves. These monochromatic waves originate as a result of a different modes of vibration of the medium, which at that time was supposed to be an electromagnetic sensitive medium called ‘ETHER’ According to well-known result of statistical mechanics, the number of such modes of vibration lying between the wavelength range $\lambda$ and $\lambda+d\lambda$ is equal to $8\pi{\lambda}^{-4}d\lambda$ per unit volume. And also according to the theorem of equipartition of energy, the total energy of a system for each mode of vibration (or degree of freedom) is equal to $kT$ , where $k$ is the Boltzmann constant and $T$ is the temperature of the system in Kelvin. Hence the total energy of the radiation lying between the wavelength range $\lambda$ and $\lambda + d\lambda$ per unit volume is
$u_{\lambda}d\lambda$ =number of mode of vibration $\times kT$
or, $u_{\lambda}d\lambda=8\pi kT{\lambda}^{-4}d\lambda$
This is Rayleigh Jean Law.

Wein’s Laws

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Various workers tried to explain the problem of energy distribution in black body radiation and finally the problem was successfully solved by German Physicist Max Planck. Before him, German Physicist Wilhelm Wein and British Physicist Lord Rayleigh & James Jean have tackled this problem and have given important laws. In fact, the work of their scientists paved the way for Planck to give his famous theory of radiation.

In this series of articles, I shall be discussing the various laws, special concentration on Planck’s law, concerning the black body in the brief.
This article is very first of the series & in I shall discuss briefly about Wein’s Laws. Other two useful topics will be discussed later.

Wein’s Formula & Wein’s Laws

The problem of black body radiation was first theoretically tackled by Wein in 1893. Besides giving a general formula for the energy distribution in the blackbody radiation, he gave following important and useful laws. Read More

What is a Prime Number?

An integer, say $p$ , [ $\ne {0}$ & $\ne { \pm{1}}$ ] is said to be a prime integer iff its only factors (or divisors) are $\pm{1}$ & $\pm{p}$ .

As?

Few easy examples are:
$\pm{2}, \pm{3}, \pm{5}, \pm{7}, \pm{11}, \pm{13}$ …….etc. This list goes up to infinity & mathematicians are trying to find the larger one than the largest, because primes numbers has no distinct pattern (as any one cannot guess the next prime after one.) As of now the biggest prime number found is  $M-47$ , called as Mersenne’s 47. This has an enormous value of $2^{43112609} -1$ . It is very hard to write it on paper because it consists of $12978189$ digits.
»M47 was Invented in 2008. Read More