Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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This question is for modern physics and wave and particle:
(a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?
Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.
Show that the ground-state hydrogen atom wavefunction is normalized. (if possible with equations and a diagram shown, thanks)
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- Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).arrow_forwardShow transcribed data (d) Find (r) and (r2) for an electron in a circular orbit of hydrogen with arbitrary prin- cipal quantum number n (corresponds to l = n - 1 and any allowed m). (e) Compute the RMS uncertainty ✓(r) – (r)2 in terms of r for the electron in part (d). Note that the fractional spread in r decreases with increasing n (in this sense the system "begins to look classical” for large n). How much more volume does a hydrogen atom in the n = 100 state occupy compared to the hydrogen atom in the ground state. (Hint - you might want to look at Griffiths 4.55, or 4.15 in the second edition)arrow_forwardThe 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_forward
- If a quantum HO (harmonic oscillator) is excited to its first excited state through absorption of light that has a wavelength of 4.33x 10-6 m, compute for another wavelength that can proceed with this equal transition when the force constant is doubled.arrow_forwardThe 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) Determine the radial probability density P(r) associated with the quantum state in question. (b) Show that the function P(r) you determined in part (a) is properly normalized.arrow_forwardFind ratio of spontaneous to stimulated emission for a cavity of temperature 50k and wavelength 0.00001arrow_forward
- Find <r> and <r^2> for a hydrogen wavefunction of state (2, 0, 0) (n = 2, l = 0, m = 0)arrow_forwardA 10 g marble is in a 1-D box of 10 cm. Assuming infinitely hard walls, (a) find its permitted energies (in J) and (b) the corresponding quantum number for the marble moving at 30 cm/s.arrow_forwardFor a hydrogen atom, determine the allowed states corresponding to the principal quantum number n = 2 and calculate the energies of these states.arrow_forward
- Calculate the transmission and reflection coefficients for an electron withkinetic energy 8 eV and potential energy 0 eV that moves into a regionwith potential energy of 5 eV.arrow_forwardCalculate the transmission coefficient for an electron of total energy 2eV incident upon a rectangular potential barrier of height 2 eV and width 10-9 marrow_forwardAn electron is trapped in a one-dimensional infinite well of width 250 pm and is in its ground state.What are the (a) longest, (b) second longest, and (c) third longest wavelengths of light that can excite the electron from the ground state via a single photon absorption?arrow_forward
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