Find the excitation energy from the ground level to the third excited level for an electron confined to a box that has a width of 360 nm?
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Find the excitation energy from the ground level to the third excited level for an electron confined to a box that has a width of 360 nm?
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- The wavelength of light emitted by a ruby laser is 694.3 nm. Assuming that the emission of a photon of this wavelength accompanies the transition of an electron from the n = 2 level to the n = 1 level of an infinite square well, compute the length L of the well.An electron in the ground state of a 1D infinite square well (width=1.222nm) is illuminated with light (wavelength=547nm). Into which quantum state is the electron excited?For a finite square well potential that has six quantized levels, if a = 10 nm (a) sketch the finite square well, (b) sketchthe wave function from x = -2a to x = +2a forn = 3, and (c) sketch the probability density for the samerange of x.
- Solve the time-independent Schrödinger equation and determine the energy levels and the wave function of a particle in the potential a? V (x) = Vol a + 2r2 with a = const.Show that the hydrogen wave function Ψ211 is normalizedAn electron is confined to a box of width 0.25 nm. Calculate the wavelengths of the emitted photons when the electron makes transitions between the fourth and the second excited states.
- The wave function of a particle in a one-dimensional box of width L is u(x) = A sin (7x/L). If we know the particle must be somewhere in the box, what must be the value of A?An electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Calculate the photon energy required to excite the electron in the ground state to the first excited state.An electron is trapped inside a 1.00 nm potential well. Find the wavelength of the photons when the electron makes a transition from n =4 to n= 1.
- An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).