Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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- Calculate the energy changes corresponding to the transitions of the hydrogen atom: (a) from n=3 to n=4 ; (b) from n=2 to n=1 ; and (c) from n=3 to n= .arrow_forwardWhat is the ground state energy (in eV) of a proton confined to a one-dimensional box the size of the uranium nucleus that has a radius of approximately 15.0 fm?arrow_forwardAssume that in the Stern–Gerlach experiment as described forneutral silver atoms, the magnetic field B has a magnitude of 0.50 T.(a) What is the energy difference between the magnetic moment orientationsof the silver atoms in the two subbeams? (b) What is thefrequency of the radiation that would induce a transition betweenthese two states? (c) What is the wavelength of this radiation, and (d)to what part of the electromagnetic spectrum does it belong?arrow_forward
- The He+ ion is a one-electron system similar to hydrogen, except that Z=2. Calculate the wavenumbers (in ) for the first and last lines in each of the three spectroscopic series corresponding to those discussed for the hydrogen atom.arrow_forwardA Hydrogen atom initially in its ground state i.e., n = 1 level, absorbs a photon and ends up in n = 4 level. (a) What must have been the frequency of the photon? Now the electron makes spontaneous emission and comes back to the ground state. (b) What are the possible frequencies of the photons emitted during this process?arrow_forwardAn electron is contained in the rectangular box , with widths Lx = 800 pm, Ly =1600 pm, and Lz= 390 pm.What is the electron’s ground-state energy?arrow_forward
- The radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius.(a) Sketch the graph of R(r) x r. For a decent sketch of this graph, take into account some values of R(r) at certain points of interest, such as r=0, 2a, 4a, and so on. Also take into account the extremes of the function R(r) and their inflection points, as well as the limit r--> infinity.arrow_forwardShow that the ground-state hydrogen atom wavefunction is normalized. (if possible with equations and a diagram shown, thanks)arrow_forwardFind <r> and <r^2> for a hydrogen wavefunction of state (2, 0, 0) (n = 2, l = 0, m = 0)arrow_forward
- For the hydrogen atom in its ground state, calculate (a) the probability density c2(r) and (b) the radial probability density P(r) for r = a, where a is the Bohr radius.arrow_forwardWhat is the probability of the electron in the 1s state of the hydrogen atom being at a radius greater than the Bohr radius a0?arrow_forwardAt time t = 0 the wave function of the hydrogen atom is: where we ignore the spin.(a) Calculate the expected value of energy for this system.(b) What is the probability of finding the system at l = 1, m = +1 as a function of time?(c) What is the probability of finding the electron around 10−10 cm from the proton, at t = 0s (canapproximate).(d) Write the time-dependent wave function: ψ (r,t)arrow_forward
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