Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 5, Problem 5.24P
To determine
(a)
The derivation of the expression for the wavelengths of the
To determine
(b)
The wavelengths of
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a) 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.)
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Chapter 5 Solutions
Modern Physics For Scientists And Engineers
Ch. 5 - Prob. 5.1PCh. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Prob. 5.17PCh. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Prob. 5.26PCh. 5 - Prob. 5.27P
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- Problem 4.2 According to quantum mechanics, the electron cloud for a hydrogen atom in the ground state has a charge density. –2r/a p(r) = where q is the charge of the electron and a is the Bohr radius. Find the atomic polarizability of such an atom. [Hint: First calculate the electric field of the electron cloud, Ee(r); then expand the exponential, assuming r « a. For a more sophisticated approach, see W. A. Bowers, Am. J. Phys. 54, 347 (1986).]arrow_forwardIt is stated without proof with respect to Bragg’s law that when the atoms are not sym- metrically disposed to the incident and reflected beams (Fig. 8.3(b)), the path difference (AB + BC) = 2dhkl sin θ . Prove, using very simple geometry, that this is indeed the case.arrow_forward1.5 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 thearrow_forward
- Express 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_forwardA hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage you would need with this apparatus to ionize the atom.arrow_forwardA proton is launched from very far away directly toward the nucleus of a Mercury atom. Ifthe initial speed of the proton is 4.0×107m/s, how close to the nucleus does it get? Take theradius of a Mercury nucleus to be 7.0 fm and assume that it remains at rest. I have tried to answer the question above, and my solution is attached. I was just wondering if the solution that I have is right? I am a bit confused about whether it would be an acceleration or a deceleration?arrow_forward
- (1) Calculate (r) and (r²) for the ground state of the hydrogen atom, expressing your answer in term of the Bohr radius. Calculate (x) and (x²) for the ground state of the hydrogen atom. Note that you really do not have to do any more work than you already did in problem #1 if symmetry properties are invoked.arrow_forwardThis question concerns the addition of 3 angular momenta (as covered in the tutorial). Consider again the hydrogen atom including the nuclear spin (1= 1/2). For an electron in a 3d level, what are all the possible values for the total angular momentum quantum number (including electron spin, nuclear spin and orbital motion)? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b с d e 1,2,3 0,1,2,3 3/2,5/2 1,3/2,2,5/2,3 1,3arrow_forwardThe three lowest energy levels of a hydrogen atom are -13.6 eV, -3.4 eV, and -1.5 eV. Assume that there is only one way to occupy any one of these levels. Calculate the relative probability that a hydrogen atom in thermal equilibrium in a star, at temperature T = 9674 K, is in its first excited state (at -3.4 eV) relative to its ground state (at -13.6 eV). Write your answer in exponential form. Recall that Boltzmann's constant can be written as 8.617 x 10-5 eV K-1.arrow_forward
- The formula for paramagnetic susceptibility is valid only if one considers the ground state of the atom. But other excited atomic levels are also present. Explain the following. a) Why is it usually permissible to disregard these higher levels when calculating the susceptibility?arrow_forwardIf the radius of the lowest energy orbit (n = 1) is 0.529 × 10-10 m, calculate the radii in m of the Bohr orbits defined by principal quantum numbers 4 and 5. (Hint use equation 1.5 and work out the overall value of the collected constants from the value of r at n = 1).arrow_forwardModel an atom as an electron confined in a rigid box of length 0.10nm. Calculate the wavelength of the emitted photon for the electronic transition from the second excited state to the ground state.Express your answer in units of nm.arrow_forward
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