Optionals IAS Mains Physics: Questions 183 - 187 of 307

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Question 183

Appeared in Year: 2005

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Essay▾

Show that the mass – energy relationship in relativistic kinematics can lead to the equation

Where is the total energy of the particle of rest mass , linear momentum and moving with velocity is the velocity of light in free space.

Explanation

Newton՚s law of conservation of momentum where is the rest mass of the body, supposed invariant in all frames of reference, is not invariant to Lorentz transformation and cannot therefore be acceptable as the correct law at relativistic velocities. What remains constant law at these high velocities and is invariant to Lorentz transformation is i…

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Question 184

Appeared in Year: 2005

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Essay▾

The wavefunction a particle confined in a cube of volume is given by

Calculate the average values of and in the region

Explanation

Solving only x part as of now:

Because x lies between

First let us solve only integral:

=

Denominator

As

(As the wavefunction is normalized)

Question 185

Fraunhofer Diffraction-Single Slit, Double Slit, Diffraction Grating, Resolving Power
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Appeared in Year: 2018

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Essay▾

2 Derive Bragg diffraction law for X-ray diffraction compare lave and Debye-Scherer methods for crystal structure determination. (Paper-2)

Explanation

In 1912, W. H Bragg put forward a model which generates the conditions for diffraction in a very simple way. They pointed that a crystal may be divided into various sets of parallel planes. The directions of diffraction lines can then be accounted for if X- rays are considered to be reflected by such a set of parallel atomic planes followed by the …

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Question 186

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Appeared in Year: 2005

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Essay▾

Write the Weizacker mass formula and explain the significance of various terms.

Explanation

Let us see how the picture of a nucleus of as a drop of liquid accounts for the observed variation of binding energy per nucleon with mass number. Each bend energy is should by two nucleons, each has a binding energy of . When an assembly of spheres of the same size is packed together into the smallest volume, as we suppose is the case of nucleon…

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Question 187

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Appeared in Year: 2005

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Essay▾

Discuss the motion of an electron in one dimensional periodic potential and show that it leads to formation of bands of allowed and forbidden states in the electron energy spectrum. How are the insulators, semiconductors and conductors discriminated on the basis of the band structure?

Explanation

The Kroing – Penny model illustrates the behaviour of electrons in a periodic potential by assuming a relatively simple one – dimensional model of periodic potential as shown in fig (1) . The potential energy of an electron in a linear array of positive nuclei is assumed to have the form of a periodic array of square wells with period of . At the b…

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