2 QuantizationA mass of m = 1.5 kg oscillates at the end of a spring with a spring constant k = 20N/m. According to Planck'shypothesis, the energy of this system is quantized: Ex = N-hfo, where h is Planck's constant, fo is the natural frequencyof the oscillator, and N is the quantum number of the oscillator.(a) What is the spacing between energy levels of the spring, AE = EN41 – Ex?(b) If the amplitude of oscillation is xo = 3.00 em, what is the approximate quantum number N of the system?(c) The energy required to ionize a hydrogen atom is 13.6 ev. Determine a mass m and a spring constant k that wouldgive this spacing between energy levels: i.e., AE = 13.6eV.(d) Critical Thinking: Based on what you have learned in this problem, why might it difficult to observe quantumeffects with everyday objects?

2 Quantization A mass of m = 1.5kg oscillates at the end of a spring with a spring constant k = 20N/m. According to Planck's hypothesis, the energy of this system is quantized: EN = N-hf9. where h is Planck's constant, fo is the natural frequency of the oscillator, and N is the quantum number of the oscillator. (a) What is the spacing between energy levels of the spring, AE = Ex41 – Ex? (b) If the amplitude of oscillation is xe = 3.00cm, what is the approximate quantum number N of the system? (c) The energy required to ionize a hydrogen atom is 13.6 ev. Determine a mass m and a spring constant k that would give this spacing between energy levels: ie.,AE = 13.6eV. (d) Critical Thinking: Based on what you have learmed in this problem, why might it difficult to observe quantum effects with everyday objects?

2 Quantization A mass of m = 1.5kg oscillates at the end of a spring with a spring constant k = 20N/m. According to Planck's hypothesis, the energy of this system is quantized: EN = N-hf9. where h is Planck's constant, fo is the natural frequency of the oscillator, and N is the quantum number of the oscillator. (a) What is the spacing between energy levels of the spring, AE = Ex41 – Ex? (b) If the amplitude of oscillation is xe = 3.00cm, what is the approximate quantum number N of the system? (c) The energy required to ionize a hydrogen atom is 13.6 ev. Determine a mass m and a spring constant k that would give this spacing between energy levels: ie.,AE = 13.6eV. (d) Critical Thinking: Based on what you have learmed in this problem, why might it difficult to observe quantum effects with everyday objects?