Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 41, Problem 45AP
(a)
To determine
The atomic diameters of the aluminum and uranium.
(b)
To determine
What would happens to the wave functions for higher atomic mass atoms.
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For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.0 mm? Assume that l has its maximum value of n - 1.
An electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV
(a)
What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the mass of an electron, 1.055 ✕ 10−34 J · s for ℏ, and note that there are 1.60 ✕ 10−19 J per eV.)
b)
What is the probability that the electron is reflected?
What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%?
c) 25.0%
d) 50.0%
Show 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)
Chapter 41 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 41.3 - Prob. 41.1QQCh. 41.3 - Prob. 41.2QQCh. 41.4 - Prob. 41.3QQCh. 41.4 - Prob. 41.4QQCh. 41.8 - Prob. 41.5QQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5P
Ch. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 13PCh. 41 - Prob. 14PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 35PCh. 41 - Prob. 36PCh. 41 - Prob. 37APCh. 41 - Prob. 39APCh. 41 - Prob. 40APCh. 41 - Prob. 41APCh. 41 - Prob. 42APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51CPCh. 41 - Prob. 52CP
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Similar questions
- Consider 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_forwardThe total probability of finding an electron in the hydrogen atom is related to the integral ∫ r2 e-2r/ao dr Where r is the distance of the electron from the nucleus and ao is the Bohr radius. Evaluate thisintegral.arrow_forwardSuppose the fractional efficiency of a cesium surface (with work function 1.80 eV) is 1.0 * 10-16; that is, on average one electron is ejected for every 1016 photons that reach the surface.What would be the current of electrons ejected from such a surface if it were illuminated with 600 nm light from a 2.00 mW laser and all the ejected electrons took part in the charge flow?arrow_forward
- An 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_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_forwardThis 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?arrow_forward
- Explain the reason that metal atomic chains have quantized G, different from bulk metals by comparing with the Schematic illustration of a diffusive and ballistic conductor.arrow_forwardExpress the complex number z1 = (√(3) + i)/2 in the form rei Φ. What about z2 = (1 + √(3i))/2? If these complex numbers are the probability amplitudes for photons to be detected, what is the probability in each case? (Hint: See attatched image for more on finding probability amplitudes)arrow_forwardWhen an atom drops from an initial level to a lower energy level or is raised from an initial level to a higher energy level, what should be the value of the energy of the photon for this to situation to happen? a. twice the energy gap between the ground and excited states b. equal to the energy gap between the ground and excited states c. less than the energy gap between the ground and excited states d. greater than the energy gap between the ground and excited statesarrow_forward
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