A physicist is watching an orangutan at a zoo swing lazily in a tire at the end

Question

A physicist is watching an orangutan at a zoo swing lazily in a tire at the end of a rope. He (the physicist) notices that each oscillation takes 3.50 s and realizes the energy is quantized.

(a) What is the difference in energy in joules between allowed oscillator states?

(b) What is the value of n for a state where the energy is 7.50 J?

(c) Can the quantization be observed? (Choices Below)

- Yes. Energy difference is large enough.

- Yes. n is large enough.    

- No. Energy difference is too large and n is too small.

- No. Energy difference is too small and n is too large.

Explanation / Answer

a) f = 1 / T = 1 / 3.50 s = 0.2857 sec-1

delta E = h f = 6.63 * 10-34 * 0.2857

= 1.89 * 10-34 J

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n = E / hf - 1/2 = E / delta E - 1 / 2

= [7.50 J / 1.89 * 10-34] - 1 / 2

= 3.97 * 1034

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No. Energy difference is too small and n is too large.

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