Calculate the expected positions of an electron in a one-dimensional box in its first, and second quantum state. The dimension of the box is 2 Å.
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Calculate the expected positions of an electron in a one-dimensional box in its first, and second quantum state. The dimension of the box is 2 Å.
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the box has width 0.7 nm. For this problem, absorption of light and subsequent relaxation connect two states (i andj) with a difference in energy, AEi E - E. (a) Calculate AEsi and AE2I for luminescence from excited energy levels to the ground state. Convert the energies to the corresponding wavelengths of light, λ31 and λ21. (b) Find the wavelength of light that corresponds to...
4. An electron is in a one-dimensional box in the n-1 state. Its energy is equal to that of a 600 nm photon. a. What is the energy of the photon? b. What is the length of the box if the electron has the same energy of the photon? c. What is the lowest energy possible for a proton in this box?
Determine for an electron in a 2 Dimensional box two pairs of quantum numbers which will cause degenerate energy given the following parameters: Lx= 2nm Ly = 3nm
2. (a) When a particle of mass 1.0 x 10-26 g in a one-dimensional box goes from the n=3 level to n=1 level, it emits a radiation with frequency 5.0 x 1014 Hz. Calculate the length of the box. (b) Suppose that an electron freely moves around inside of a three-dimensional rectangular box with dimensions of 0.4 nm (width), 0.4 nm (length), and 0.5 nm (height). Calculate the frequency of the radiation that the electron would absorb during its transition...
Calculate the probability of exciting an electron in a one-dimensional box (actually a nanoscale wire) to the n 2 excited state if the box is 10.0 nm long and the temperature is 410.0 K. For the one- dimensional box, En = n2t2h2/(2ma2) and the levels are non-degenerate (but remember that the energy should be measured relative to the ground state). For this example, T2h/(2mea2) is equal to 1.381- 10 23 JK-1 J and the partition function is 2.44. kB 6.02-10-22...
Consider an electron in a one-dimensional box of length 0.16 nm. (a) Calculate the energy difference between the n = 2 and n = 1 states of the electron. (b) Calculate the energy difference for a N2 molecule in a one-dimensional box of length 11.2 cm.
An electron is trapped in a one-dimensional infinite well and is in its first excited state. The figure indicates the five longest wavelengths of light that the electron could absorb in transitions from this initial state via a single photon absorption: λa = 81.5 nm,λb = 31.1 nm,λc = 19.5 nm,λd = 12.6 nm, and λe = 7.83 nm. What is the width of the potential well? III-(nm)
Suppose that an electron trapped in a one-dimensional infinite well of width 118 pm is excited from its first excited state to the state with n = 8. (a) What energy (in eV) must be transferred to the electron for this quantum jump? The electron then de-excites back to its ground state by emitting light, In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths (in...
What is the probability per unit length that an electron in the first excited state of a one-dimensional box is in the center of the box? What about for the second excited state?
> I think we can do it by using E=n^2 h^2/(8ma^2)
Shahana Wed, Nov 10, 2021 9:14 AM