Consider a harmonic oscillator with mass m 0.100 kg and k- 50 N/m. You may have

Question

Consider a harmonic oscillator with mass m 0.100 kg and k- 50 N/m. You may have worked similar problems before, as a mass on a spring using dassical mechanics, but this time you will use the solution to the Schrödinger equation for the harmonic oscillator. Keep in mind that this system would be enormous by quantum standards, and in practice you would never expect to use quantum mechanics to describe a mass on a spring. Nonetheless, it is interesting to see what quantum mechanics predicts here. Let this oscillator have the same energy as a mass on a spring, with the same k and m, released from rest at a displacement of 5.00 cm from equilibrium What is the quantum number n of the state of the harmonic oscillator? Express the quantum number to three significant figures. View Available Hint(s) Throughout this problem, use h 1.055 x 10-*Js Submit Part B This question will be shown after you complete previous question(s).

Explanation / Answer

a)

Energy of harmonic oscillator is

E = 1/2kx^2

E = 1/2 x 50 x (0.05)^2

E = 0.0625 J

The frequency of oscillator is

f = 1/2pi*sqrt(k/m)

f = 1/2pi*sqrt(50/0.1)

f = 3.56 Hz

the number of quantum state of harmonic oscillator is

n = En / hf

n = 0.0625 J / (6.626 x 10^-34 J-s x 3.56 Hz)

n = 2.65 x 10^31

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