• Pintu Mandal

      Articles written in Resonance – Journal of Science Education

    • Symmetry Energy in the Semi-empirical Mass Formula: A Review

      Sagnik Mondal Pintu Mandal

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      Symmetry energy in the semi-empirical mass formula appears as a correction term, and it can be explained in the classroom in various ways. One can explain it using the elementary idea that the term is proportional to some power of the difference in the neutron and proton numbers, and the binding energy is maximum when these numbers are equal for a given mass number. Other approaches follow the Fermi gas model that treats the neutrons and protons as degenerate gases inside the nucleus. Using an intuitive approach, it is explained that the symmetry energy originates due to a change in the total kinetic energy of the degenerate nucleons as the neutron number deviates from the proton number in a nucleus of a given mass number. A detailed analytical calculation presents that the total kinetic energy of degenerate nucleons contributes to both the volume and symmetry energy terms and thus reduces the nuclear binding energy. The contribution of the potential energy of the nucleons to the symmetry energy is also discussed in this article. Our calculations estimate the associated coefficient of the symmetry energy term, which is found to be close to the existing value.

    • Statistical Thermodynamics of an Ideal Gas: General Expressions of Some Properties

      Nath Santu Pintu Mandal

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      Using the fundamental approach of statistical mechanics anddistribution formulae, we study some well-known thermodynamic properties of an ideal gas in any positive dimensionality and with anypositive-exponent dispersion relation. We have derived generalexpressions for the density of states and canonical partition functionfollowing the formalism of classical statistics and have calculatedproperties like average energy, average pressure, entropy, etc., foran ideal classical gas. The general expression for the density ofstates and quantum statistical distribution functions are used todetermine the general expressions for the thermal de Broglie wavelength,critical temperature and critical wavelength for an ideal Bose gas and the Fermi energy, Fermi wavelength, average energy for an ideal Fermigas. These properties are compared with what we commonly find instandard textbooks for a nonrelativistic ideal gas of materialparticles or massless particles like photons in three dimensions.

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