Optionals IAS Mains Physics: Questions 194 - 199 of 307

Close packed structures are mostly found in monatomic crystals having non- directional bonding, such as metallic bonding. In these structures, the coordination number of each atom is 12, i.e.. each atom is surrounded by 12 similar and equal size neighbors. Out of these twelve neighbors, six lie in one plane, there in an adjacent parallel plane abov…

Let us consider the problem of finding the centre of mass for the two particles system shown below.

If we try to balance the system on a pivot at a point in between and both particles exert torques that tend to tip the beam, rotating it around the pivot. In order to balance the system on the pivot, we wa…

In nearly free electron (NFE) model, it is assumed that the crystal potential is so weak that the electron behaves essentially like a free particle. The effects of the potential are then treated by the use of perturbation methods, which should be valid in as much as the potential is weak. This model should serve as a sough approximation to the vale…

We have only to prove by the help of Lorentz transformations.

Where and are the coordinates of the same event observed by two observes in system while is moving with a velocity relative to

Let us consider the expression

(Putting value of from Lorentz transformation)

Thus, we have proved that

That is, the expression is invariant under Lorentz tra…

The propagation of light in an optical fibre from one of its ends to the other is based on the principle of total internal reflection. When light enters one end of the fibre, it undergoes successive total length of the fibre along a zigzag path, as shown in fig. (1) . A small fraction of light may escape through sidewalls but a major fraction emerg…

The phase relation between the waves emitted by two independent light sources rapidly charges with time and therefore they can never be coherent, through the sources are identical in all respects. However, if two sources are derived from a single source by some device, then any phase change occurring in one source is simultaneously accompanied by t…