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FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
11th Edition
ISBN: 9781119459132
Author: Halliday
Publisher: WILEY
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Question
Chapter 39, Problem 39P
To determine
To find:
Verify that the radial probability density for the ground state of the hydrogen atom is normalized.
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Chapter 39 Solutions
FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS
Ch. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3QCh. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10Q
Ch. 39 - Prob. 11QCh. 39 - Prob. 12QCh. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3PCh. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61PCh. 39 - Prob. 62PCh. 39 - Prob. 63PCh. 39 - Prob. 64PCh. 39 - A diatomic gas molcculc consistsof two atoms of...Ch. 39 - Prob. 66PCh. 39 - Prob. 67PCh. 39 - Prob. 68PCh. 39 - Prob. 69PCh. 39 - Prob. 70PCh. 39 - An old model of a hydrogen atom has the charge e...Ch. 39 - Prob. 72PCh. 39 - Prob. 73P
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Similar questions
- An electron is in an angular momentum state with /= 3. (a) What is the length of the electron's angular momen- tum vector? (b) How many different possible z compo- nents can the angular momentum vector have? List the possible z components. (c) What are the values of the angle that the L vector makes with the z axis?arrow_forwardEstimate the ground state energy of helium atom by taking the product of two normalized hydrogenic ground state wave functions as the trial wave function, the nuclear charge Ze being the variable parameter. Assume that the expectation value of the interelectronic repulsion term is (5/4) ZWH, WH = 13.6 eV?arrow_forwardA spin state of an electron in the vector form is given by 3i X = A 4 %3D (a) Determine the normalization constant A, assuming it to be real and positive. (b) Write down the x using the X+ and X-. If z-component of the spin of the electron is measured, what is the probability of finding the value in +ħ/2? (c) Determine the expectation value and uncertainty of S? in terms of h when the electron is in spin state x. Justify your answer. (d) Determine the expectation value of the product S?S, in terms of h when the electron is in spin state X.arrow_forward
- What is the smallest value that ℓ may have if L is within 10° of the z axis?arrow_forward(4) Electronic energy level of a hydrogen atom is given by R E ; n = n2 1, 2, 3,... and R = 13.6 eV. Each energy level has degeneracy 2n² (degeneracy is the number of equivalent configurations associated with the energy level). (a) Calculate the partition function Z for a hydrogen atom at a constant temperature. (b) Let us consider that the energy level of a hydrogen atom is approximated by a two level system, n = 1,2. Estimate the mean energy at 300 K.arrow_forwardB) A spin state in an arbitrary direction is given by directions. Cas 2 -io sin 2 Find the form of the states in z, x and yarrow_forward
- For hydrogen atoms in a d state, sketch the orbital angular momentum with respect to the z axis. Use units of U along the z axis and calculate the allowed angles of L with respect to the z axis.arrow_forwardCompute 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 ΔΕarrow_forwardCompute the most probable distance of the electrom from the nucleus for theground state of a hydrogen-like atom or ion as a function of Z, the atomic number ofthe atom or ion.arrow_forward
- Calculate the possible z components of the orbital angular momentum for an electron in a 3p state.arrow_forwardIf we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?arrow_forwardProve that the total degeneracy for an atomic hydrogen state having principal quantum number n is 2n2.arrow_forward
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