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- Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.Calculate the linear momentum of photons of wavelength 350nm. At what speed would a H2 molecule need to travel for it to have the same linear momentum? Pphoton =(mv) H₂ (zamu)(1.66 x 10-27 kg/amu) = mH₂kg Kg421) The moment of inertia of an SF, molecule is 3.07 x 10 kg m. What is the minimum energy needed to start it rotating?
- 6. The general expression for the density of quantum states D(e) as a function of energy & under periodic boundary conditions is D(e) = V dSe (2π)3 VkE' 7³ / = 1 where Vke is the gradient of e with respect to k, fdSe represents the integral over a surface of constant energy in k-space, and V is the volume of the system in the real space. Find the density of states for a two-dimensional quantum system with εακCalculate the relative populations of two quantum statesseparated by an energy of 0.4 × 10-21 J if the temperatureis 25°C.The rotational constant of 1H35CI is 317.8 GHz. What is the separation of the lines in its pure rotational spectrum (a) in gigahertz. (b) in reciprocal centimetres?
- 2. A one-particle, one-dimensional system has the state function y=(sinat) ()* e/² + (cosat) (32/C) 1/4 2 1/4 e-x²/² е πρ >-x2/c2 xe where a is a constant and c = 2.000 Å. If the particle's position is measured at t = 0, estimate the probability that the result will lie between 2.000 Å and 2.001 Å.J.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.A 1.00 kg weight is traveling at a constant velocity of 10.0 ms-1, in a cubic room 3.00 m on an edge.(a). Determine the sum of the squares of its three quantum numbers.(b). What would be the ground state energy for this weight?
- The moment of inertia of CH4 can be ca lcu lated from the expression I= 8/3 MHR2 where R = 109 pm is the CH bond length. Ca lcu late the minimum rotational energy (other than zero) of the molecule and the degeneracy of that rotational state.4) Calculate the energies E of the first three rotational levels (those giving the minimal energy) of 1H35Cl molecule that is free to rotate in three dimensions. For its moment of inertia I = μeffR2 use the effective mass with μeff = mH * mCl / (mH + mCl) and bond length R = 127 pm.4. The variance of many measurements of observable A is given by o = (A²) – (A)². Derive the variance in the measurements of position of a particle in a box in state „(x).