General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 28, Problem 49E
To determine
The probability of the electron to be at a radius greater than that permitted by classical physics.
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Calculate the probability of an electron in the 2s state of the hydrogen atom being inside the region of the proton (radius ≈ 1.2 x 10-15 m). Repeat for a 2p electron.
Calculate the probability of an electron in the ground state of the hydrogen atom being inside the region of the proton (radius = 1.2 x 10-15 m).
Compute the intrinsic line-width (AX) of the Lyman a line (corresponding to the n = 2 to n = 1) transition for the Hydrogen atom. You may
assume that the electron remains in the excited state for a time of the order of 10 s. The line-width may be computed using:
e hc
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Chapter 28 Solutions
General Physics, 2nd Edition
Ch. 28 - Prob. 1RQCh. 28 - Prob. 2RQCh. 28 - Prob. 3RQCh. 28 - Prob. 4RQCh. 28 - Prob. 5RQCh. 28 - Prob. 6RQCh. 28 - Prob. 7RQCh. 28 - Prob. 8RQCh. 28 - Prob. 9RQCh. 28 - Prob. 10RQ
Ch. 28 - Prob. 1ECh. 28 - Prob. 2ECh. 28 - Prob. 3ECh. 28 - Prob. 4ECh. 28 - Prob. 5ECh. 28 - Prob. 6ECh. 28 - Prob. 7ECh. 28 - Prob. 8ECh. 28 - Prob. 9ECh. 28 - Prob. 10ECh. 28 - Prob. 11ECh. 28 - Prob. 12ECh. 28 - Prob. 13ECh. 28 - Prob. 14ECh. 28 - Prob. 15ECh. 28 - Prob. 16ECh. 28 - Prob. 17ECh. 28 - Prob. 18ECh. 28 - Prob. 19ECh. 28 - Prob. 20ECh. 28 - Prob. 21ECh. 28 - Prob. 22ECh. 28 - Prob. 23ECh. 28 - Prob. 24ECh. 28 - Prob. 25ECh. 28 - Prob. 26ECh. 28 - Prob. 27ECh. 28 - Prob. 28ECh. 28 - Prob. 29ECh. 28 - Prob. 30ECh. 28 - Prob. 31ECh. 28 - Prob. 32ECh. 28 - Prob. 33ECh. 28 - Prob. 34ECh. 28 - Prob. 35ECh. 28 - Prob. 36ECh. 28 - Prob. 37ECh. 28 - Prob. 38ECh. 28 - Prob. 39ECh. 28 - Prob. 40ECh. 28 - Prob. 41ECh. 28 - Prob. 42ECh. 28 - Prob. 43ECh. 28 - Prob. 44ECh. 28 - Prob. 45ECh. 28 - Prob. 46ECh. 28 - Prob. 47ECh. 28 - Prob. 48ECh. 28 - Prob. 49ECh. 28 - Prob. 50ECh. 28 - Prob. 51ECh. 28 - Prob. 52ECh. 28 - Prob. 53ECh. 28 - Prob. 54E
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- An atom with 2 neutrons, 1 proton, 1 electron, is in its ground state when one of its neutrons undergoes a nuclear decay β (n → p + e + ν). The produced electron is fired at high speed, while the proton remains confined in the nucleus, forming a Helium nucleus with the original electronspinning around him. Find the probability that the ion resulting from He + is in the state 1S.arrow_forwardCalculate the probability of finding the electron in the 1s state outside spheres of radius 0.75a0, 2.5a0, and 4.5ao. Inspect the results and make an argument for what you think would be a good definition for the "size" of the Hydrogen atom.arrow_forwardAssume that the nucleus of an atom can be regarded as a three-dimensional box of width 2·10-14 m. If a proton moves as a particle in this box, find: (a) The ground-state energy of proton in MeV. (b) The energies of the first and second excited sates. (c) What are the degenerates of these states?arrow_forward
- Compute the intrinsic line-width (Δλ) of the Lyman α line (corresponding to the n=2 to n=1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10^−8s. The line-width may be computed using:ΔE=(hc/λ^2)Δλarrow_forwardThe wave function for H-atom in 1s state is given below. Explain the radial probability density of H-atom in 1s state and also write an expression for the same. Sketch schematically the plot of this vs. radial distance.arrow_forwardAn electron is trapped in a one-dimensional region of length 1.00 x 10-10 m (a typical atomic diameter). (a) Find the energies of the ground state and first two excited states. (b) How much energy must be supplied to excite the electron from the ground state to the sec- ond excited state? (c) From the second excited state, the electron drops down to the first excited state. How much energy is released in this process?arrow_forward
- The nucleus of a gold atom has a radius of 7.0 fm. Estimate the kinetic energy of a proton or neutron confined to a gold nucleus. Hint :Use HEISENBERG PRINCIPLE to find Linear Momentum of Neutron or Proton with uncertainity in position equals to radius 7.0 fm.arrow_forwardDetermine the integral | P(r) dr for the radial probability density for the ground state of the hydrogen atom 4 P(r) = - r²e-2rla a³ O 1 O-1 O 0.5arrow_forwardIn atoms there is a finite, though very small, probability that, at some instant, an orbital electron will actually be found inside the nucleus. In fact, some unstable nuclei use this occasional appearance of the electron to decay by electron capture. Assuming that the proton itself is a sphere of radius 1.1 * 10-15 m and that the wave function of the hydrogen atom’s electron holds all the way to the proton’s center, use the ground-state wave function to calculate the probability that the hydrogen atom’s electron is inside its nucleus.arrow_forward
- The 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_forwardAssume that the nucleus of an atom can be regarded as a three-dimensional box of width 2:10-¹4 m. If a proton moves as a particle in this box, find (a) the ground-state energy of proton in MeV and (b) the energies of the first excited state. (c) What are the degenerates of these states? Constants: h = 6.626-10-34 [J-s], m = 1.673-10-27 [kg] and ħ=h/2π.arrow_forwardWhat is the answerarrow_forward
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