(a) A muon is in a one-dimensional square potential well. The muon is in the n = 3 state. The potential energy at the bo

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A A Muon Is In A One Dimensional Square Potential Well The Muon Is In The N 3 State The Potential Energy At The Bo 1 (85.66 KiB) Viewed 170 times

(a) A muon is in a one-dimensional square potential well. The muon is in the n = 3 state. The potential energy at the bottom of the well is zero and the walls are separated by 2.00 × 10-8 m. (i) Suppose that the potential energy at the top of the well is infinite. The solution of the wavefunction is a standing wave. Calculate the wavelength of this standing wave. (ii) Now suppose that the potential energy at the top of the well is finite, but still higher than the total energy of the muon. Sketch the wavefunction of the muon. Label the positions of the walls of the potential well on your sketch. (iii) For the same situation as in part (ii), now sketch the probability of detecting the muon at a given position. (b) Now consider a muon that is trapped in a cubic box with sides of length 2.00 × 10-8 m. The muon is initially in the state with quantum numbers n₁ = 5, n₂ = 1 and n3 = 1. The mass of a muon is 1.88 x 10-28 kg. (i) Calculate the energy of the muon in this state. (ii) Show that this energy level has a degeneracy of 4. (iii) The muon relaxes from this state into its ground state. As it does so, it emits a single photon. Calculate the wavelength of the emitted photon.