Organic Chemistry
6th Edition
ISBN: 9781936221349
Author: Marc Loudon, Jim Parise
Publisher: W. H. Freeman
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Question
Chapter 1, Problem 1.14P
Interpretation Introduction
Interpretation:
The plot of the wavefunction
Concept introduction:
The wavefunction
The point at which the probability of finding an electron is zero is known as the node. The two types of nodes are radial nodes and angular nodes.
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A particle freely moving in one dimension x with 0 ≤ x ≤ ∞ is in a state described by the normalized wavefunction ψ(x) = a1/2e–ax/2, where a is a constant. Evaluate the expectation value of the position operator.
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What values of J may occur in the terms (i) 3D, (ii) 4D, (iii) 2G? How many states (distinguished by the quantum number MJ) belong to each level?
Chapter 1 Solutions
Organic Chemistry
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10P
Ch. 1 - Prob. 1.11PCh. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Prob. 1.21APCh. 1 - Prob. 1.22APCh. 1 - Prob. 1.23APCh. 1 - Prob. 1.24APCh. 1 - Prob. 1.25APCh. 1 - Prob. 1.26APCh. 1 - Prob. 1.27APCh. 1 - Prob. 1.28APCh. 1 - Prob. 1.29APCh. 1 - Prob. 1.30APCh. 1 - Prob. 1.31APCh. 1 - Prob. 1.32APCh. 1 - Prob. 1.33APCh. 1 - Prob. 1.34APCh. 1 - Prob. 1.35APCh. 1 - Prob. 1.36APCh. 1 - Prob. 1.37APCh. 1 - Prob. 1.38APCh. 1 - Prob. 1.39APCh. 1 - Prob. 1.40APCh. 1 - Prob. 1.41APCh. 1 - Prob. 1.42APCh. 1 - Prob. 1.43APCh. 1 - Prob. 1.44APCh. 1 - Prob. 1.45APCh. 1 - Prob. 1.46APCh. 1 - Prob. 1.47APCh. 1 - Prob. 1.48APCh. 1 - Prob. 1.49AP
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- The ground-state wavefunction for a particle confined to a one dimensional box of length L is Ψ =(2/L)½ sin (πx/L) Suppose the box 10.0 nm long. Calculate the probability that the particle is: (a) between x = 4.95 nm and 5.05 nm (b) between 1.95 nm and 2.05 nm, (c) between x = 9.90 and 10.00 nm, (d) in the right half of the box and (e) in the central third of the box.arrow_forwardTo what speed must a proton be accelerated from rest for it to have a de Broglie wavelength of 100 pm? What accelerating potential difference is needed?arrow_forwardNormalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the particle is restricted to move in one dimensional box of width ‘a’.arrow_forward
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