Engineering physics 3(Relaxation time, Temperature dependence of Electrical Resistivity)
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This document discusses engineering physics and was authored by Mr. Gouri Kumar Sahu, a senior lecturer in physics. It covers topics including the interpretation of relaxation time, the temperature dependence of electrical resistivity, and drawbacks of the classical free electron theory. The key points are that relaxation time in metals is on the order of 10-14 seconds due to electron-phonon interaction, resistivity is proportional to temperature according to theory but experimentally proportional to T, and the classical theory fails to explain several phenomena like ferromagnetism and superconductivity.
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![2 ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics.
2 ENGINEERING PHYSICS
Mr. Gouri Kumar Sahu
Sr. Lecturer in Physics.
SESSION-4
4.1 Interpretation of Relaxation time
From eq[2.3],
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Let the electric field is switched off at t=0, then the drift velocity gradually falls
to zero, due to scattering by phonons. Integrating above equation
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The relaxation time is determined by the electron phonon interaction in the
metal.
It is of the order of 10-14 sec.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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The speed of light has practical applications in a variety of fields, including telecommunications, navigation, and satellite technology. For example, the time it takes for a signal to travel from a satellite to the Earth is used to calculate the distance between the satellite and the Earth.
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The expansion of the universe was first observed by Edwin Hubble in the 1920s when he discovered that the light from distant galaxies was redshifted, which is an effect that is caused by the expansion of space. This observation led to the development of the Big Bang theory, which proposes that the universe began as a singularity, or a point of infinite densi
7
This document summarizes the synthesis and luminescence study of Europium-doped Lanthanum Aluminate phosphor. The phosphor was prepared using a modified solid state reaction method and characterized using photoluminescence and thermoluminescence techniques. Photoluminescence excitation showed peaks at 264nm and 314nm, while emission showed intense peaks at 594nm and 619nm. Thermoluminescence glow curves were recorded at different UV exposure times, with the highest intensity peak obtained at 10 minutes exposure. Kinetic parameters of the phosphor such as activation energy and frequency factor were evaluated using peak shape analysis.
Probing Molecular Electronic Structure Using High Harmonic Generation Tomography
The structure of valence electronic orbitals of a molecule determines the majority of chemical properties. Generation of high-order harmonic frequencies from atomic sources has been directly related to the electronic structure of the atom, (1) and extended as far as tomographic reconstruction of linearly symmetric polyatomic molecular systems with some success. (2,3,4)
However, because of the increased resolution of these reconstructions, discrimination of fine details of the orbital reconstructions reveals some inconsistencies in the orbital shapes when compared with past models & theoretical calculations. (2) There are several proposed corrections to the Strong Field Approximation (SFA) that currently underlies tomographic reconstruction as well as all other experiments that use high harmonic generation (HHG) to probe molecular systems. (5,6,7)
---------------------------------------------------------------------
1. Lewenstein et al. Phys Rev A 49 (3) 1994.
2. Salieres, Maquet, Haessler, Caillat, Taieb. Rep. Prog. Phys. 75 (2012) 062401.
3. Li, Liu, Yang, Song, Zhao, Lu, Li, Xu. Opt. Ex. 21 (6) 2013. 7599.
4. Torres et al. Phys Rev. Lett. 98 (2007) 203007.
5. Diveki et. al. J. Chem Phys. 414 (2013) 121.
6. Yip, Palacios, Rescigno, McCurdy, Martin. J. Chem Phys 414 (2013) 112.
7. Spanner, Patchkovskii. J. Chem. Phys. 414 (2013) 10.
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- 2. 2 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. 2 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-4 4.1 Interpretation of Relaxation time From eq[2.3], డழ௩ೣவ డ௧ ௦௧௧. ൌ െ ழ௩ೣவ ఛ Let the electric field is switched off at t=0, then the drift velocity gradually falls to zero, due to scattering by phonons. Integrating above equation න ߲ ൏ ݒ௫ ൏ ݒ௫ ൌ െ න ߲ݐ ߬ ݈݊ ൏ ݒ௫ ൏ ݒ௫ሺ0ሻ ൌ െ ݐ ߬ ,ݎ ൏ ݒ௫ ൌ൏ ݒ௫ 0 ݁ି ௧ ఛ ሾ3.2ሿ The relaxation time is determined by the electron phonon interaction in the metal. It is of the order of 10-14 sec.
- 3. 3 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. 3 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-4 4.2 Temperature Dependence of Electrical Resistivity 4.2 Temperature Dependence of Electrical Resistivity Kinetic energy associated with an electron is 1 2 ݉ሺܿ̅ሻଶൌ 3 2 ݇ܶ When an electric field is applied, the resulting acceleration ܽ ൌ ா . If the mean free path is ߣ, then the time between collision is ఒ ̅ . Hench the drift velocity acquired before next collision is ݑ ൌ ݈ܽܿܿ.ൈ ݁݉݅ݐ ൌ ݁ܧ ݉ ߣ ܿ̅ Thus the average drift velocity is ݑ 2 ൌ ݁ܧ 2݉ ߣ ܿ̅
- 4. 4 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. 4 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-4 4.2 Temperature Dependence of Electrical Resistivity 4.2 Temperature Dependence of Electrical Resistivity If n is the number of electrons per unit volume, then current density is ܬ௫ ൌ ݊݁ݑ 2 ൌ ݊݁ଶܧ 2݉ ߣ ܿ̅ Or ߪ ൌ ܬ௫ ܧ ൌ ݊݁ଶ 2݉ ߣ ܿ̅ Or, ߩ ൌ 2݉ ݊ߣ݁ଶ ൈ 3݇ܶ ݉ ൌ 12݉݇ܶ ݊݁ଶߣ െെെെെെ െሾ3.3ሿ Here it is assumed that ߣ is independent of temperature. Hence ߩ ∝ ܶ which is contradictory to the experimental fact that ߩ ∝ ܶ.
- 5. 5 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. 5 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. SESSION-4 4.3 Drawbacks of Classical free electron theory 4.3 Drawbacks of Classical free electron theory 1) ߩ is proportional to ܶ. But experimentally it was found that ߩ is proportional to T. 2) K/ ߪܶ= L, a constant (Wiedmann-Franz law) for all temperatures. But this is not true at low temperatures. 3) The theoretically predicted value of specific heat of a metal does not agree with the experimentally obtained value. 4) This theory fails to explain ferromagnetism, superconductivity, photoelectric effect, Compton effect and blackbody radiation.
- 6. 6 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. 6 ENGINEERING PHYSICS Mr. Gouri Kumar Sahu Sr. Lecturer in Physics. END OF SESSION -4 SESSION-4 THANK YOU