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11 Nov 2019
Quantum
Derive the Rydberg constant R_y following Bohr's model for the hydrogen atom. Start with the assumption that the Coulombic force is equal to the centripetal force needed for a circular orbital, e^2/4 pi epsilon_0 r^2 = mv^2/r. Use this to find an expression for the total energy E = KE + V, where the kinetic energy KE = 1/2 mv^2 and the potential energy V = -e^2/4 pi epsilon_0 r. Finally, use the assumption that the orbital circumference is equal to an integer number of de Broglie wavelengths, or 2 pi r = nh/(mv), to find E_n = -R_y/n^2 , where n is an integer.
Quantum
Derive the Rydberg constant R_y following Bohr's model for the hydrogen atom. Start with the assumption that the Coulombic force is equal to the centripetal force needed for a circular orbital, e^2/4 pi epsilon_0 r^2 = mv^2/r. Use this to find an expression for the total energy E = KE + V, where the kinetic energy KE = 1/2 mv^2 and the potential energy V = -e^2/4 pi epsilon_0 r. Finally, use the assumption that the orbital circumference is equal to an integer number of de Broglie wavelengths, or 2 pi r = nh/(mv), to find E_n = -R_y/n^2 , where n is an integer.
Irving HeathcoteLv2
4 Nov 2019