Using Thomas-Fermi method, derive an expression for the total kinetic energy of N electrons in a cubic box of side L, and hence obtain the expression for pressure.
The Thomas-Fermi model provides a semiclassical approximation to describe the distribution of electrons in an atom, or more generally, in a system of many electrons. It treats the electron density as a continuous function rather than dealing with individual electrons explicitly. This model can also be applied to a system of N electrons confined in a cubic box of side (L), allowing us to estimate quantities like the total kinetic energy and the resulting pressure. In the Thomas-Fermi method, we consider electrons as forming a degenerate Fermi gas at zero temperature. The electrons occupy all quantum states up to the Fermi energy (E_F). In momentum space, the allowed states form a sphere of radius (p_F), the Fermi momentum. For a system of (N) electrons confined in a cubic box of volume _____ _______ ___ ______ ________ ____.
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Write the laser rate equation for a two level system and hence prove that the steady state population inversion cannot be achieved in a two level system.
i) The fundamental vibrational frequency of a molecule occurs at . Determine the position of Raman line if the molecule is excited with a laser of wavelength
.
The spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
The anti-symmetric spin function for a two electron system is given as:$
Prove that is an eigenfunction of
.
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and gas temperature of
. Obtain the ratio of spontaneous and stimulated emission if the wavelength is
.
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