visualizing the orbital wave functions of the hydrogen atom (20 points) for the n = 1, 2, 3 ground, first excited, and second excited states | nem) with angular momentum eigenstates em) =丨1. m), rewrite them using yitl(θ, φ) (10) (a). verify that these states are still orthogonal to one another. what must the a, be to insure that the new wave functions lpi) are both real and orthonormal? (b) now do this for the le, m-2. m) angular momentum states. that is form (12) (13) (14) (15) (16) verify that they are orthogonal to one another, and choose the five a; values so that they are all real and normalized note that we have used the spectroscopic notation: s, p, d, etc. for the 1 = 0,1,2, etc. angular momentum states. does the notation x, y, 2 for the p-orbitals and a2 -y2, ay, xz, yz, and 3z2 -72 for the d-orbitals make sense to you? explain (c). now for the fun part: form spherical 3d plots of the square of the orbital part of the wave function with 1 = 0 (s), 1-1 (pr, dxy, dxz, d, and d322-/2). (note that the s orbital is just yo, the number1 times its normalization constant.) that is, for the py orbital a mathematica script to make a spherical 3d plot of the square of the normalized py orbital wave function is py, pz), and 2 (d, a-j-, sphericalplot3d [(3/(4 pi)) * sin [theta * sin [theta] sin [phi| * sin [phi] (theta, 0, pi), {phi, 0, 2 pi), plotrange-all (17)
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Physics, 22.06.2019 10:00
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Physics, 22.06.2019 12:00
Aboat radioed a distress call to a coast guard station. at the time of the call, a vector a from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. a vector from the station to the point where the boat was later found is = 30.0 km, 15.0° north of east. what are the components of the vector from the point where the distress call was made to point where the boat was found? in other words, what are the components of vector c = b - a?
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Consider two regions of space containing a static electric field, region a and region b. in region a the equipotential lines are more closely spaced than those in region b. what can be said about the relative strength of the electric field in the two regions? a) the electric field in region a is stronger th
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Athin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. a) what is the magnitude of the electric field due to the rod at z = 0? n/c (b) what is the magnitude of the electric field due to the rod at z = infinity? n/c (c) in terms of r, at what positive value of z is that magnitude maximum? r (d) if r = 4.00 cm and q = 9.00 µc, what is the maximum magnitude? n/c
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visualizing the orbital wave functions of the hydrogen atom (20 points) for the n = 1, 2, 3 g...
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