EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 38, Problem 7Q
To determine
Whether the statement "the ground-state energy in the hydrogen atom can be precisely known but that the excited states have some uncertainties in their values" remains consistent with the uncertainty principle kept in its energy form.
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- 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?arrow_forwardCan the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain.arrow_forwardConsider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forward
- 6. An electron in hydrogen atom is in initial state Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211) where wnim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? hw = - n2 c. Write the state Þ(r, t) at time t, using energy eigenvalues as En d. Find the expectation value of L in the state Þ(r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of Lz led to the value –ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities?arrow_forwardPhysics What is the energy of a photon that could cause an electron to transition from the ground state to the n = 6 energy level in an infinite well of width L = 2nm ?arrow_forward3. a) According to the spherical shell model, predict J" for the ground state and first excitation of 'Be, ¹70 and 2¹Ne. b) Explain pros and cons of the shell model based on a harmonic oscillator potential of the type: Vo = 1/2 kr².arrow_forward
- 3. a) Show that for values of n » 1, the fractional difference in energy between states n and n + 1 for a particle in an infinite potential well is approximately given by En+1 – En En b) What is the percentage difference between states n = 1000 and n = 1001? c) Discuss how this result is related to the Bohr correspondence principle.arrow_forward1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?arrow_forwardWhat is the total mechanical energy for a ground- state electron in H, He*, and Li++ atoms? For which atom is the electron most strongly bound? Why?arrow_forward
- 01: Choose the correct answer: a) The zero point energy of the 1-dimensional harmonic oscillator is: 1) hw, 2) zero 3)-hw.. b) The wave function has definite parity when the potential is: 1) symmetric 2) infinite 3) antisymmetric. c) In ô-function potential the bound states are founds when the energy of the particle (E) is: 1) E 0 3) E-0 3) L/2n. d) The wavelength associated with a particle in 1-D box of length L is: 1) 2L/n 2) L/n ay e) At boundary condition is always continuous except where: 1) V(x) = 2) V(x)=0 2) n=0 3) V(x)=constant. 3) n=00 1) n=1 f) The zero point energy of the 1-dimensional box occurred with: g) In classically forbidden regions, the wave function behavior is: 1) oscillatory 2) decay or grow exponentially.arrow_forward2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe approximated as 2 =(n * (n + )' En hw ;n = 0,1,2,... (++) = The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such oscillators is given by C = Nk [(1-u² + *)+ 4x (: + *)]. 240 80 Note that the correction term here increases with temperature.arrow_forwardThe lifetimes of the levels in a hydrogen atom are of the order of 10-8 s. Find the energy uncertainty of the first excited state and compare it with the energy of the state. 3 p ROarrow_forward
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