A mass of m= 1.5 kg oscillates at the end of a spring with a spring constant k = 20 N/m. According to Planck's hypothesis, the energy of this system is quantized: EN=N-hfo, 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 = EN+1-EN? (b) If the amplitude of oscillation is xo = 3.00 cm, 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: i.e., AE = 13.6 eV. (d) Critical Thinking: Based on what you have learned in this problem, why might it difficult to observe quantum effects with everyday objects?

A mass of m= 1.5 kg oscillates at the end of a spring with a spring constant k = 20 N/m. According to Planck's hypothesis, the energy of this system is quantized: EN=N-hfo, 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 = EN+1-EN? (b) If the amplitude of oscillation is xo = 3.00 cm, 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: i.e., AE = 13.6 eV. (d) Critical Thinking: Based on what you have learned in this problem, why might it difficult to observe quantum effects with everyday objects?