Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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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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Assume 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
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these states? Constants: h = 6.626-10-34 [J-s], m = 1.673-10-27 [kg] and ħ=h/2π.
An electron is in a spin state given by
2
to = √² (¹/²)
|x)
3
Find the probability that a measurement of Sy will yield the value +ħ/2.
Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 156.
Express your answer in units of ℏ to three significant figures.
Chapter 39 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
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_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_forwardWhat 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_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
- The expectation value of the z-co-ordinate,, in the ground state of the hydrogen atom (wave function: 100(r) normalization constant and ao is the Bohr radius), is Ae-Tlao, where 'A' is the 0.25 ao 0.5 ao aoarrow_forwardFor 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_forwardCalculate the possible z components of the orbital angular momentum for an electron in a 3p state.arrow_forward
- 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 ΔΕarrow_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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