In terms of the ground-state energy E1,1,1, what is the energy of the highest level occupied by an electron when 10 electrons are placed into a cubical box?
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In terms of the ground-state energy E1,1,1, what is the energy of the highest level occupied by an electron when 10 electrons are placed into a cubical box?
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- Chapter 39, Problem 009 Suppose that an electron trapped in a one-dimensional infinite well of width 144 pm is excited from its first excited state to the state with n 9. (a) What energy 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 that can be emitted? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number UnitsAn electron is trapped in an infinitely deep one-dimensional well of width 0,251 nm. Initially the electron occupies the n=4 state. Suppose the electron jumps to the ground state with the accompanying emission of photon. What is the energy of the photon?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).The energies in a 2D particle-in-a-box are given by h² 8mL 2 in which the box is a square enclosure with Lx = Ly = L, and nx, ny = 1, 2, 3,... . (a) If the particle is an electron and L = 300 pm (assume three significant figures), find the value of the lowest energy level in units of 10-18 J (that is, if the energy is 5.00 × 10-18 J, you would report it as "5.00"). E n, n (n₂ ² + n₂²) y x yA particle is in the n = 9 excited state of a quantum simple harmonic oscillator well. A photon with a frequency of 3.95 x 1015 Hz is emitted as the particle moves to the n = 7 excited state. What is the minimum photon frequency required for this particle to make a quantum jump from the ground state of this well to the n = 8 excited state? (Give your answer in Hz.)
- A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4ϵ, 9ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ =0.035 eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature isA hypothetical molecule oscillates with a natural frequency of 1.4 × 1013 Hz. Part (a) What is the energy difference, in electron volts, between adjacent harmonic oscillator states of the hypothetical molecule? Part (b) What is the quantum number of the state of the hypothetical molecule that has an energy of 0.75 eV? Round your answer to the nearest integer.