Question

please showing steps for questions 3,4,5 and 6 please i would appreciate it.

kg the gap of adjacent levels is 4.81 x 10". Problem 3. For a particle of mass m 1.33 x 10 Calculate the force constant. (20.9 kg/s) - Problem 4. Calculate the wavelength of a photon needed to excite a transition between neighboring energy levels of a harmonic oscillator of mass equal to that of a proton and force constant 855 Nm 1 (Newton N; 1 Nxm1]). Proton mass is 1.67262158 x 10 kg (7.54x103) Problem 5. Evaluate a characteristic vibrational wavenumber and a turning point, X., for 'H"clif an angular vibration frequency, w, is 5.634x10's! Problem 6. Show that the Hermite polynomials multiplied by a bell-shaped Gaussian function for VO are indeed the eigenfunctions for a one-dimensional linear harmonic oscillator and obtain their corresponding eigenvalues. Can you show it for v=1 and 2?

Answer 1

. 7 constat) 3 Given m= 1. 381026 ug. 4€ = 4.81 X10-21 J The gap of adjacent level is AE = Eore - Ex := tw = to a ::ww porn on his face constant. on hit = AE x = loss x1034 IS (Planck's on ka m (46.2 = 1:3310 26 0g (4 to 10 J .1-33x10 26 KW x 20.787 x10726 kg ~ 27.6 ang kanyang -:| K = 27.6 mg I got k=27.6 hy not 20.9 kg . Here the frocess expression & Values i put connectly and got 27-6 hy TO

The transition occure is DE = E (Photon) how = no = ne - = x= anem = 27 x 3x10 m variomx/1. 67262158x10-27 ng - 855 = 18.54x108 1.9563x10-30 $xm = 96- 35 x 108 x 10's on = 26-35 x 10-7m ~ 2.64 x10m 2.64 MM wavelength of the Photon is 2.64 mm (CM). (Please post in dividual question. )