The wavefunctions for a particle in a box are given by: ψn(x) =
(2/L)^1/2
sin(nπx/L), with n=1,2,3,4. . . .
Let’s assume an electron is trapped in a box of length L = 0.5 nm.
(a) Light of what wavelength is needed to
excite the electron from the ground to the first excited state? (b)
Will that wavelength increase or decrease,
if you exchange the electron with a proton? Why?
The wavefunctions for a particle in a box are given by: ψn(x) = (2/L)^1/2 sin(nπx/L), with...
While studying the particle in a box in this chapter, you CR come up with what you think is a brilliant idea. Suppose the electron in the hydrogen atom is modeled like a par- ticle in a one-dimensional box! You look online and learn that the transition from the first excited state of hydrogen to the ground state emits a photon of wavelength 121.6 nm. (a) From this information, you determine the size of the box in which the electron...
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...
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...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
2. Consider an electron in a 1D potential box (V(x) = 0 for 0<x<L, V(x) = co otherwise) of length L = 1 nm. The electron is described by the wave function, c) = Jasin ( (a) Using the appropriate Hamiltonian derive an expression for the kinetic energy of the electron (5 marks) (b) Calculate the energy (in Joules) of the transition between the ground state and the 1 excited state. [3 marks]
Consider an electron in a cubic box that measures 1nm on an edge a) Calculate the energy difference between the ground and first excited states and compare this energy difference with KbT at 300 K. b) Using the Boltzman factor, Nx=N0 exp (-delta E/KbT), calculate and comment on the relative population of the first excited state at this temperature. c) What minimum wavelength is required to excite the electron into the the first excited state d) How would you answer...
Answer all questions please 5. Consider a particle in the first excited state ofa rigid box of length a. (a) Find the probability density (b) where is the particle most likely to be found? 6. Determine the wavelength of the photon emitted when an electron in a hydrogen atom makes transition from the 5 excited state to the following states (a) ground state (b) 1 excited states (c) 2 excited state Determine whether the emission is visible, uv or infrared...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
For the particle with a mass m in a box with a length of 1 nm, a) Write Schrodinger’s equation b) Write the integral expression for the probability of finding the first excited state between 0.1 nm and 0.5 nm