EM Energy U₂ Figure 82.1 S Energy EM UM Figure B2.2 Energy Energy h√/k/m hy/ky/m h√k/m h√/k/m Ground state Us √k./m Figu

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Em Energy U Figure 82 1 S Energy Em Um Figure B2 2 Energy Energy H K M Hy Ky M H K M H K M Ground State Us K M Figu 1 (70.33 KiB) Viewed 41 times

EM Energy U₂ Figure 82.1 S Energy EM UM Figure B2.2 Energy Energy h√/k/m hy/ky/m h√k/m h√/k/m Ground state Us √k./m Figure B2.3 Figure B2.1 shows the potential energy curve, Us, as a function of oscillation amplitude, s, for a classical mass-spring oscillator (with an offset, Eu). Figure B2.2 shows the Morse potential, Um, for a diatomic molecule as a function of the separation of the atoms. Figure B2.3 shows the potential energy curve for a mass-spring quantum oscillator where only certain values of the total energy (U+K) can occur physically, as indicated by the energy levels shown. (a) (3 marks) Figure B2.1 illustrates a classical oscillator where the total energy, whatever its value may happen to be for a given amplitude of oscillation, is conserved. What does energy is conserved mean and what can you say about the kinetic energy during a single period of oscillation operating at a particular amplitude s as a consequence of energy conservation? Refer to figure B2.1 in your answer. (b) (4 marks) Attaching a mass of 0.050 kg to a relaxed spring hanging vertically stretches the spring by 0.040 m at equilibrium. What is the spring constant of the spring and what will the period of the oscillator be when it is set in motion? (c) (3 marks) It is often said that a diatomic molecule can be modelled as a classical mass spring oscillator. With reference to Fig. B2.2, or otherwise, explain why this is the case, and also for what conditions such a model is valid for a diatomic model. (d) (3 marks) Most materials expand when their temperature increases. With reference to one of the figures above explain physically why thermal expansion occurs. (e) (4 marks) An experimenter has a meter that can measure energy. It has a specification such that it can measure an amount of energy of 2.5 x 10 J, or more, with accuracy and precision. They plan to use this to prove that a quantum oscillator with an effective spring constant of 570 Nm¹ has discrete energy levels. Calculate a suitable upper limit on the mass of the quantum oscillator (such as in figure B2.3) that needs to be used in the experiment to lead to a result which will demonstrate the quantised nature of the energy levels. Include text with your answer to explain your calculations. (f) (3 marks) What will be the photon energies, and the corresponding wavelengths, of the two lowest energy photons that can be emitted by a quantum oscillator with the upper limit on its mass described in (e)?