Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 8, Problem 34P
(a)
To determine
The expression for the probability as a function of
(b)
To determine
The value of
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A typical diameter of a nucleus is about 10-14 m. Use the infinite square-well potential to calculate the transition energy from the first excited state to the ground state for a proton confined to the nucleus. Of course, this is only a rough calculation for a proton in a nucleus.
1.5
The time-averaged potential of a neutral hydrogen atom is given by
- ar
Ф
4 TTE0
ar
1 +
2
r
where q is the magnitude of the electronic charge, and al =
Bohr radius. Find the distribution of charge (both continuous and discrete) that will
give this potential and interpret your result physically.
ao/2, ao being the
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Chapter 8 Solutions
Modern Physics
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8 - Prob. 1QCh. 8 - Prob. 2QCh. 8 - Prob. 3QCh. 8 - Prob. 4QCh. 8 - Prob. 5QCh. 8 - Prob. 6Q
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 34P
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- Problem 7: The electric potential near a hydrogen atom can be modeled as the equation to the right where ao is the Bohr radius and q is the charge on the central proton. V (r) exp(- 2r/a,)(1 +a/r) Randomized Variables m = 2 n = 3 Part (a) Find an expression for the 0-component of the electric field, Eg. Numeric : A numeric value is expected and not an expression. Eg = Part (b) Find an expression for the o-component (azimuthal) of the electric field, Eo Expression : Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, b, c, d, g, h, j, k, m, P, S, t Part (c) What is the change in the magnitude of the electric field (in N/C) if a test point moves from the position (x = m²ao, y = 0, z = 0) to position (x = n-ao, y = 0, z = 0). Numeric : A numeric value is expected and not an expression. ΔΕ Ξarrow_forwarda) An electron and a 0.0500 kg bullet each have a velocity of magnitude 460 m/s, accurate to within 0.0100%. Within what lower limit could we determine the position of each object along the direction of the velocity? (Give the lower limit for the electron in mm and that for the bullet in m.) b) What If? Within what lower limit could we determine the position of each object along the direction of the velocity if the electron and the bullet were both relativistic, traveling at 350c measured with the same accuracy? (Give the lower limit for the electron in nm and that for the bullet in m.)arrow_forwardConsider a very simplistic model of atomic nucleus in 1D: a proton is completely localized in a 1D box of width L = 1.00 × 10¬14m. In other words, the proton wavefunction outside of the "nucleus" is zero. Note that L represents a typical nuclear radius. (A) What are the energies of the ground and the first excited states? If the proton makes a transition from the first excited state to the ground state, what is the angular frequency of the emitted photon? (B) What is the probability that the proton in its ground state (i.e., the lowest energy state) is not found in the distance L/12 around each boundary of the box? (C) Using the uncertainty principle, derive a minimum possible value on the momentum uncertainty in the second state above the ground state. (D) Compare your answer to the previous question (B) to probability distribution one would obtain for a classical particle. First argue about how the probability distribution would look for a classical object in its ground state. How…arrow_forward
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