CAN A PENCIL AND A TAPE FETCH YOU A NOBEL PRIZE?

Yes, it did for Andre Gelm and Konstantin Novoselev in 2004. We know pencil contains graphite lead -a form of carbon. They took a pencil and draw a line on a cello tape. The line is made up of layers and layers of bonded carbon atoms. They took another tape; put it on the drawn line; then peeled it off. Now, the half of carbon-layers stick to the second tape and came off with it. They took yet another piece of tape and repeated the process. The number of layers in the very first tape reduced further. They repeated the procedure again and again. Finally, they are left with just one single layer of carbon-atoms. It is just one atom thick. The atoms are arranged in a hexagonal lattice as shown in the figure. It is graphone which has the potential to become wonder material of the future.

Graphene is stronger than steel. It is the thinnest material known to man. It is an excellent conductor of heat and electricity.
We will see some applications of graphene.
When we filter sea-water through graphene, we instantly get drinkable salt-less water.
A battery stores a lot of energy but takes a long time for charging. A capacitor charges quickly but stores only less electrical energy. The graphene-based super-capacitor solves this problem. Tomorrow we may be able to charge our smartphones and laptops in minutes.
When graphene is used in smartphone screen, the price will further fall down.
Solar cells made using graphene will also be cheaper.

Graphene seems to cure many technical ills we face today. But commercial mass production of graphene is not still successful. We hope that we will be blessed with more graphene in the future.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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