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Vibrations of the hydrogen molecule
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- The energy levels of the Bohr model for the atom can be expressed mathematically as En -13.6 eV, where Z is the atomic number, and n is the quantum number. This model is reasonably accurate for hydrogen and for singly ionized helium. The photon associated with the transition of an electron from the ground state to the first excited state in singly ionized helium has a different wavelength than that associated with a similar transition in hydrogen. Which of the following correctly describes the wavelengths of these two photons in terms of the energy level diagrams for hydrogen and helium? The photon absorbed by hydrogen has a longer wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. B The photon absorbed by hydrogen has a shorter wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. The photon…arrow_forwardSolid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = ħwn n = 0, 1, 2,... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ħw = = 224 KB and the system vibrational partition function is given by 3N Z ² = la₁ - (1 1 e-0/T). (a) If the system contains one mole of atoms, find the average energy (in J) of this system at T= 172 K. (You can use = BkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).arrow_forwardAn atom of iron has a radius of 156. pm and the average orbital speed of the electrons in it is about ×5.7*10^7 m/s. Calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of iron. Write your answer as a percentage of the average speed, and round it to 2 significant digits.arrow_forward
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