Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 36, Problem 45P
To determine
To show: that the electron is most likely to be found at one Bohr radius.
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Calculate the probability that the electron in the hydrogen atom, in its ground state, will be found between spherical shells whose radii are a and 2a, where a is the Bohr radius.
For a hydrogen atom, determine the allowed states corresponding to the principal quantum number n = 2 and calculate the energies of these states.
For the hydrogen atom in its ground state, calculate (a) the probability density c2(r) and (b) the radial probability density P(r) for r = a, where a is the Bohr radius.
Chapter 36 Solutions
Essential University Physics
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 11ECh. 36 - Prob. 12ECh. 36 - Prob. 13ECh. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34ECh. 36 - Prob. 35ECh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Solar physicists measure the strong magnetic...Ch. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
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- For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forwardFor a 3d electron in an external magnetic field of 2.50 × 10-3 T, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque.arrow_forwardWrite the election configuration for iron.arrow_forward
- Write an expression for the total number of states with orbital angular momentum l.arrow_forwardConsider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forwardShow that the group velocity for a nonrelativistic free electron is also given by , where is the electron’s velocity.arrow_forward
- What is the probability that in the ground state of the hydrogen atom, the electron will be found at a radius greater than the Bohr radius?arrow_forwardFor what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.0 mm? Assume that l has its maximum value of n - 1.arrow_forwardGiven a H atom in its 1s state, compute the probability that the electron is found within 0 and 1.8 armstrong from the nucleus. SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAYarrow_forward
- The wavefunction for an electron in the Hydrogen atom is provided in figure 1, where B is a constant, and a0 is the Bohr radius. By inspection and using the angular part of the wavefunction, identify the value of the quantum numbers l and ml, then operate on this wavefunction with Lˆz, and use your result to verify the value of ml identified.arrow_forwardCalculate 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.arrow_forwardThe product of the two provided equations (with Z = 1) is the ground state wave function for hydrogen. Find an expression for the radial probability density and show that the expection value for r (for the ground state) is <r> = 3a0/2.arrow_forward
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