In a nanoscale experiment, an atom is confined to an infinitesimally small volume in which its partition function, z, has a value of 6. A second experiment confines three of these atoms in the same volume. What is the value of Z for this new system? 18 216 06 24 36
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The partition function is distribution of n particles in k energy levels
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- Q²- A system of two energy levels E, and E₁ is populated by N particles at temperature T. The particles populate the energy levels according to the classical distribution law. (a) Derive an expression for the average energy per particle. (b) Compute the average energy per particle vs the temperature as T → 0 and T → co (c) Derive an expression for the specific heat of the system of N particles (d) Compute the specific heat in the limits T→ 0 and T → ∞o.If density of mercury is 13600 kg/ m = 9.8 m/s?. Find the energy of translation 3 and g %3D per cubic metre of oxygen at N.T.P.A) By what factor is the uncertainty of the electron's position(1.36×10-4 m) larger than the diameter of the hydrogen atom?(Assume the diameter of the hydrogen atom is 1.00×10-8 cm.) B) Use the Heisenberg uncertainty principle to calculate Δx for a ball (mass = 122 g, diameter = 8.50 cm) with Δv = 0.425 m/s. C) The uncertainty of the (above) ball's position is equal to what factor times the diameter of the ball?
- The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one. What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?Answer the following. (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). 1s22s22p11s22s22p2 1s22s22p31s22s22p41s22s22p51s22s22p6 (b) Write out the values for the set of quantum numbers n, ℓ, m, and ms for each of the electrons in nitrogen. (In cases where there are more than one value, enter the positive value first. Enter positive values without a '+' sign in front of them. Include all possible values.) 1s states n = ℓ = m = ms = ms = 2s states n = ℓ = m = ms = ms = 2p states n = ℓ = m = ms = ms = m = ms = ms = m = ms = ms =Which of the following observations is not related to the Pauli Exclusion Principle? O the electronic wave function is antisymmetric with respect to particle exchange O angular momentum is conserved in quantum mechanical systems O if two electrons are in the same orbital, they are spin-paired Ospatial orbitals can contain no more than two electrons
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