# Month: February 2011

## Rayleigh- Jean’s Law

Image via Wikipedia

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

Image via Wikipedia

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.

# 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

# Albert Einstein

This name need not be explained. Albert Einstein is considered to be one of the best physicists in the human history.

The twentieth century has undoubtedly been the most significant for the advance of science, in general, and Physics, in particular. And Einstein is the most luminated star of the 20th century. He literally created cm upheaval by the publication, in quick succession, in the year 1905, two epoch-making papers, on the concept of the photon and on the Electrodynamics of moving bodies respectively, with yet another on the Mathematical analysis of Brownian Motion thrown in, in between.

The Electrodynamics of moving bodies was the biggest sensation and it demolished at one stroke some of the most cherished and supposedly infallible laws and concepts and gave the breathtaking new idea of the relativity of space and time.

## Derivative of x squared is 2x or x ? Where is the fallacy?

As we know that the derivative of $x^2$ , with respect to $x$ , is $2x$.

i.e., $\dfrac{d}{dx} x^2 = 2x$

However, suppose we write $x^2$ as the sum of $x$ ‘s written up $x$ times..

i.e.,

## Solving Ramanujan’s Puzzling Problem

Consider a sequence of functions as follows:-

$f_1 (x) = \sqrt {1+\sqrt {x} }$
$f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }$

$f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } }$

……and so on to

$f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n \sqrt {x} } } } } }$

## Its a Mystery! – Simulacrum in Eagle Nebula

Of all the exotic & strangest photos ever taken from outer space, the most curious ones are of Eagle Nebula. According to the images received through various space cameras, Eagle Nebulae appear to made of gaseous clouds and they give birth to new stars. Eagle Nebulae are named after their bird alike shape.

First taken through Hubble, when this photo was first shown on CNN, hundreds of responses came in from people reporting that they could see a face in the cloud. When the color of the photo was adjusted, a large human form seemed to appear within the cloud.  Couldn’t you see a human (or a wolf-man) in above image? As Eagle Nebulae are more productive and quite younger than other Nebula types, they were named ‘Star Queen Nebula‘ later.

Researchers argued such illusions to be incidental. As clouds can take any shape, Eagle Nebulae do the same too. The Nebula clouds work as same as water clouds do. The one major difference is only that one yields stars and latter yields  water. NASA occasionally updates eagle nebula images and each time, a simulacrum appears. This is still a mystery.