Question

(10 pts) The two calculations below pertain to the quantum harmonic oscillator (qho). Relevant expressions for the qho states and energies needed are given by: En-(n +-)ћ1_ and n-AnHn(ye- Two 1g masses are attached by a spring with a force constant k-500 kg/s2. Calculate the zero point energy of this system. How fast would this system have to move to have that much translational energy? a. b. Calculate the wavenumber and wavelength of radiation absorbed when a quantum harmonic oscillator with a frequency of 3.15x1013 s1 makes a transition from the n 2 to the n-3 state. In what portion of the electromagnetic spectrum does this radiation lie?

Answer 1

@ For zero point ensgy no in the enungy expression a) top Zero poinl rugg ry th : 耂. 2. For two 4g mares, the reclu c d mm is given by → m, m m, + m Here, K 500 kgs Eo 方ニ1-05X10-59 JS -34 500 2 5 x 10-4 시 5.25 x01 Joule 5 32 Let' the speed ofthe system required to Aave the transla,onal arungy same ao the kero point uungs express10ル 아가ransfrh orta trungy 2. Hence, AV 5.25 x 103 to 5o x Io 32 5 x 10-4 1.449 X10 | 4 m/s 1.45X10^ 14 rn/s m/s There fork, the system would have to move with a speed of 1-45 x 10-4

㈧ave number opHAe radiah ~. an be om the wave number 3 X108 1 05 x tom105 x lo em1 3

& the wavelength of the ransltion is given Sinco, the avelength is in behu een 2.5-50,um → it will reside in the middle infrared regier of tke electrmagnatc speetrum CtromA C specTrom.