. An electron in a long organic molecule used in a dye laser behave approximately like a particle in a box with width 4.18 nm. (a) What is the λ of the proton emitted when the electron undergoes a transition from the first excited level to the ground level. (b) What is the λ of the proton emitted when electron undergoes a transition from the second excited level to the first excited level?

. An electron in a long organic molecule used in a dye laser behave approximately like a particle in a box with width 4.18 nm. (a) What is the λ of the proton emitted when the electron undergoes a transition from the first excited level to the ground level. (b) What is the λ of the proton emitted when electron undergoes a transition from the second excited level to the first excited level?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 7.4CYU: Check Your Understanding A sodium atom nukes a transition from the first excited state the wound...

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Check Your Understanding A sodium atom nukes a transition from the first excited state the wound state, emitting a 589.0-nm photon with energy 2.105 eV. If the lifetime of this excited state is 16108s, what is the uncertainty in energy of this state? What is width of the corresponding line?
When a quantum harmonic oscillator makes a transition from the (n+1) state to the n state and emits a 450-nm photon, what is its frequency?
3. In a particular semiconductor device, an oxide layer forms a barrier 0.6 nm wide and 9V high between two conducting wires. An electron beam is accelerated through a 4V potential so that each electron approach the barrier with an energy of 4 eV. (a) What percent of the incident electrons will tunnel through the barrier? (b) Is aa for this system much larger than one, much less than one, or the same order of magnitude as one? Can we approximate the transmission coefficient using the formula below? - 16 (1-E) e E Vo T= 16; e-2aa (1) (c) Find the transmission coefficient using Eq. 1 and compare with your answer from part (a). Was Eq. 1 a good approximation?
a) What is the wavelength of light emitted by an Electron transitioning from the 4th energy state in the Balmer Series? b) What Energy does a photon at this wavelength have?
a) Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol. b) Is this transition in the visible spectral domain? If not, in which region is it located?
Electron diffractometers help us understand the structure of matter. Material is covered in an array of parallel nano-scale metal wires with unknown spacing. A beam of electrons, accelerated through a potential of 20.80 kV produces a pattern of electron impacts on a distant screen with a central bright peak with two smaller peaks. The angular position of the smaller peaks is 25.20 degrees relative to the central peak. What is the spacing of the wires? You may treat the electron as non-relativistic. (Answer in meters)
(a)What are the energies of the first three energy levels of an electron confined in a one-dimensional box of wavelength 0.70nm. Give your answer in electron volts (eV) (b) How much energy must the electron lose to move from the n=2 energy level to the n=1 energy level? Again, give your answer in eV. (c) Suppose that an electron can move from the n=2 level to n=1 level by emitting a photon of light. If energy is conserved, what must the photon wavelength be? Give your answer in nanometers
An electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.45 eV. (a) What is the length L of the region? nm(b) What energy input is required to promote the electron to its first excited state? eV
An electron is in an infinite square well of width 2.0 nm. What is the wavelength of the emitted photon in nanometers as the electron transitions from the n=8 to the n=4 state? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19J). Please give your answer with no decimal places.
One can now use integrated-circuit technology to manufacture a "box" that traps electrons in a region only a few nanometers wide. Imagine that we make an essentially one-dimensional box with a length of 3 nanometers. Suppose we put 10 electrons in such a box and allow them to settle into the lowest possible energy states consistent with the Pauli exclusion principle. a) What will be the value of the highest energy level occupied by at least one electron? b) What will be the electrons' total energy (ignoring their electrostatic repulsion)? c) How would your answers to the above be different if the electrons were bosons instead of fermions? d) What is the wavelength of the lowest energy photon that can be absorbed (the electrons in this box are fermions)?
The electrons within the T-system of conjugated hydrocarbons may be treated as particles confined within a one-dimensional box. The lowest energy transition in the spectrum of a polyene hydrocarbon corresponds to excitation of an electron from the highest occupied energy level to the lowest unoccupied level. If the hydrocarbon contains 6 electrons and has a spectral transition at a wavelength of 278 nm, estimate the effective length of the TT-system. The estimated length = nm. Hint: you will need to fill the energy diagram to know which energy levels are involved in the transition. me = 9.110 x 1031 kg (Enter in e-notation, e.g. 1.23e-4, tolerance ±5%)
A certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?