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?
What is the probability per unit length that an electron in the first excited state of...
5. (25 pts) An electron is trapped inside a rigid box of length L-0.250nm. a) If the electron is initially in the second excited state, what is the wavelength of the emitted photon if the electron jumps to the ground state? b) The wavefunction for the electron in its first excited state is given by-(x)fsin2m excited state is given by ψ(x)--sin what is the probability of finding the electron in the middle region of the rigid box, srsc) Sketch the...
7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if it is in the (a) the ground state (b) the first excited state. (c) Compare these probabiliies to the classical probability. (d) What is the average value for the position in the ground state? Do your answers make sense? 15P 7. What is the probability of finding a particle translating in the central third of a 1 dimensional box if...
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...
7. We have an electron trapped in a one dimensional box, and is excited to the 2nd (n = 2) state. What will be the length of the box if our electron has the same energy as a violet photon (404 nm)?
An electron is confined to a one-dimensional infinite well. From experiment, the first excited state is measured to have an energy 1.2 eV above the ground state. What must be the width of the well?
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)
a)Compute the energy separation between the ground and second excited states for an electron in a one-dimensional box that is 7.40 angstroms in length. Express the energy difference in kJ⋅mol−1. b)Compute the wavelength of light (in nm) corresponding to this energy.
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!) By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!)
What is the length of a one-dimensional box if an electron requires a wavelength of 6350 nm to be excited from the n = 2 to the n = 3 energy level?
(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to estimate the minimum kinetic energy of an electron in this state, assuming that the uncertainty in position equal to it's diameter. (Note: Relativistic corrections are not necessary). b.) Assuming this excited electron only remains in this state for 0.1 ns, before emitting a photon and returning to...