1. A hydrogen atom is in the state: Y(r) = = 1 √10 (322 +2221 + 2i220 + 11-1) What is the probability of finding the hydrogen atom in states? (n = 3, l = 2, m = 2), (n = 2, l = 2, m = 1), (n = 2, l = 2, m = 0), (n = 1, l =
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- Chapter 39, Problem 044 A hydrogen atom in a state having a binding energy (the energy required to remove an electron) of -1.51 eV makes a transition to a state with an excitation energy (the difference between the energy of the state and that of the ground state) of 10.200 eV. (a) What is the energy of the photon emitted as a result of the transition? What are the (b) higher quantum number and (c) lower quantum number of the transition producing this emission? Use -13.60 eV as the binding energy of an electron in the ground state. (a) Number Units (b) Number Units (c) Number Units15 b. Suppose an electron is in a spin state given by x = A(). 8i Find i. the normalization constant A ii. (S.) iii. (S.) and iv. the probability that a measurement of S, will yield h/2.3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:
- 4. Show that the wave functions for the ground state and first excited state of the simple harmonic oscillator, given by W0 (x) and W1 (x), are orthogonal, where %(x) = Aoe¬max² /2h 4 (x) = A1V m@ -mox² /2h -xe8. If 4(x) = D sin 17x, what is the probability density for the range L 0 to L? Show calculations.2. Consider the states of hydrogen atom given by (n, l, m) where n a. What is the maximum value of l? If L² is measured what is the maximum possible value that can be obtained? b. What is the maximum value of L₂?
- Needs Complete typed solution with 100 % accuracy.7 The fundamental vibrational wavenumber ( ṽ) for 1H 127I molecule is 23096 cm-1 A. Determine the force constant (k) of 1H 127I B. Calculate the value of for 2H 127I. Show all calculations and the units. Explain the reasoningPhysics 1. Derive the expression ε(ω)=1- ωp 2 / ω2 , ωp2 =ne2 /ε0m for the dielectric constant as a function of ω for a free electron gas of number density n. 2. Show clearly that metals are opaque to light for which ω is less than ωp. 3. Calculate the wavelength cutoff for Na metal if the volume of a primitive unit cell in Na is 35×10-30 m3 how to solve this problem?