1. Refer to the Table below that lists the first few spherical harmonics YM. Suppose we subject a linear rigid molecule to z-polarized microwave radiation. Show explicitly that the Y→ Yº rotational transition is allowed while the Y→ Y₂ transition is not allowed. TABLE 6.3 The first few spherical harmonics. YOU 1 (4x)¹/2 3 Y₂¹ Y₂² 1/2 Y = 87 1/2 x² = (15) (3 cos²0-1) 1/2 = sin Be 15 87 15 327 sin cos le-¹ 1/2 sin²Ge-24 Y₁ = Y₁¹ = 3 87 15 87 Y₂ = Y² = (3 15 1/2 32π cos 9 1/2 1/2 sin gel sin cos e 1/2 sin² 0e²

1. Refer to the Table below that lists the first few spherical harmonics YM. Suppose we subject a linear rigid molecule to z-polarized microwave radiation. Show explicitly that the Y→ Yº rotational transition is allowed while the Y→ Y₂ transition is not allowed. TABLE 6.3 The first few spherical harmonics. YOU 1 (4x)¹/2 3 Y₂¹ Y₂² 1/2 Y = 87 1/2 x² = (15) (3 cos²0-1) 1/2 = sin Be 15 87 15 327 sin cos le-¹ 1/2 sin²Ge-24 Y₁ = Y₁¹ = 3 87 15 87 Y₂ = Y² = (3 15 1/2 32π cos 9 1/2 1/2 sin gel sin cos e 1/2 sin² 0e²

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Solid state physics question: Plot a dispersion curve for longitudinal vibrations in a 1D crystal with a basis of two atoms at each lattice point. Justify the values you used to generate the curve.
Problem 2. Calculate the wavelength of light emitted in the 2P/2 1S/2 transition of the real hydrogen atom (in- cluding the fine structure correction). The values of the quantum numbers n, I and j follow from the spectroscopic notation nL, and the letters S, P,D and F corresponds to l = 0, 1,2, 3 respectively. Spin value is always 1/2 for the hydrogen atom. Express your answer in Angstroms.
2
2) Critical magnetic fields of a certain superconductor are experimentally measured as 0.175 T at 15 K and 0.700 T at 12 K. a) Calculate the transition temperature. b) Calculate critical fields at 0 Kand 8 K 2) Critical magnetic fields of a certain superconductor are experimentally measured as 0.175 T at 15 K and 0.700 T at 12 K. a) Calculate the transition temperature. b) Calculate critical fields at 0 K and 8 K.
QUESTION 2 a. i. State Laue condition. Refer to Fig.2. Draw a complete vector diagram to show the Laue condition for the given Bragg's plane (Lattice plane). Draw all the related vectors and show the origin of reciprocal lattice and valid reciprocal lattices. Based on the diagram determine the magnitude of vector G in term of magnitude of vector T. (21/2m) Lattice plane (hkl) Incident wave vector Ко Atom Atom Figure 2
1. Enumerate the microstates of p3. Determine the MS and ML values for each microstate. 2. On a table of possible MS and ML values, tally the microstates in no. 1 for a particular combination of MS and ML 3. Based on the table in no. 2, determine the atomic term symbols for the allowed atomic states of p3 resulting from the coupling of orbital and spin angular momentums. 4. Arrange the term symbols in no. 3 according to increasing energy.
Physics written by hand.
Below is the LCAO for the sp3 hybrid orbital. What is the value for the c²? (The answer mus be a number, not a fraction) Ya = C($25 +02p₂ +$2p, + $2p:) 2Px
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 reasoning
2. Spinors and rotations (a) For a function f(ø) that can be expanded in a Taylor series, show that f(o +4) = e²L±p/hf(6) where p is an arbitrary angle. For this reason, Lz/ħ is called the generator of rotations about the z-axis. More generally, L.ân/ħ is the generator of rotations about the direction în, in the sense that exp(iL.ng/h) effects a rotation through angle y (in the right hand sense) about the axis în. In the case of spin, the generator of rotations is S.în/ħ. In particular, for spin 1/2., X = ei(oî)g/2x tells us how spinors rotate. (b) Construct the (2x2) matrix representing rotation by 180° about the x-axis and show it converts spin up (x+) spin down (x-) as you would expect. (c) Construct the matrix representing the rotation by 90° about the y-axis, and check what it does to X+· (d) Construct the matrix representing rotation by 360° about the z-axis. Discuss the meaning of the answer. (e) Show that ei(o-î)e/2 = cos(p/2) + i(în · o) sin(4/2)
Physics 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?
Consider a two-electron spin system in a singlet state. a. If a measurement of one of the electrons shows that it is in a state with sz = 1/2, what is the probability of obtaining another state with sz= +1/2? b. If a measurement of one of the electrons shows that it is in a state with sx = 1/2, what is the probability of obtaining another state with sy = +1/2?