Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN: 9781305079113
Author: David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher: Cengage Learning
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Chapter 5, Problem 6P

Using Table 5.2, write down the mathematical expression for the 2 p x wave function for an electronically excited H atom. Estimate the probability of finding the 2 p x electron if you look in a cubical box of volume of 0. ( pm ) 3 centered at a distance of 0. 5 00 × 1 0 1 0 m in the θ = π / 2 , ϕ = 0 direction. Does this probability change as you change ϕ ? At what ϕ angles is the probability of finding the electron smallest and at what ϕ angles is the probability the largest? (Note that ϕ = 2 π is the same location as ϕ = 0 , so don’t double count.)

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Moseley’s law states that if we plot the square root of the frequency of the Kα X-ray photons from various targets against the atomic number Z of the target, the graph is linear given by √f = a(Z−b) where a and b are constants called proportionality and screening (or shielding) constants. For Kα series, the value of a is √(3Rc/4) and that of b is 1. Here R is Rydberg's constant and c is speed of light. Find the wavelength of the Kα X-ray photons when the target is Molybdenum. A) 194 pm B) 72 pm C) 154 pm         D) none of these
Part B The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using En=(n^2h^2)/8mL^2, ? = 1, 2, 3, … where L is the length of the 1D chain. Assuming L = a0(N – 1), where N is the number of Na atoms and a0 = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enough (Hint: assume that each Na only contributes 1 electron to the problem and consider the information in Question 1c above.). b) Thermal energy at room temperature is 4.15 × 10–21 J. Calculate the minimum number of Na atoms required so that the energy gap is smaller than the thermal energy.
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Chapter 5 Solutions

Principles of Modern Chemistry

Ch. 5 - Calculate the average distance of the electron...Ch. 5 - The helium ion He+ is a one-electron system whose...Ch. 5 - Spectroscopic studies show that Li can have...Ch. 5 - Spectroscopic studies of Li also show that...Ch. 5 - Spectroscopic studies show that Na can have...Ch. 5 - Using data from Problems 13 and 15, calculate the...Ch. 5 - Give the ground-state electron configurations of...Ch. 5 - Give the ground-state electron configurations of...Ch. 5 - Prob. 19PCh. 5 - Write ground-state electron configurations for the...Ch. 5 - Identify the atom or ion corresponding to each of...Ch. 5 - Identify the atom or ion corresponding to each of...Ch. 5 - Predict the atomic number of the (as yet...Ch. 5 - (a) Predict the atomic number of the (as yet...Ch. 5 - Suppose that the spin quantum number did not...Ch. 5 - Suppose that the spin quantum number had three...Ch. 5 - Photoelectron spectra of mercury (Hg) atoms...Ch. 5 - Quantum mechanics predicts that the energy of the...Ch. 5 - Prob. 29PCh. 5 - Photoelectron spectroscopy studies of silicon...Ch. 5 - Photoelectron spectroscopy studies have determined...Ch. 5 - Prob. 32PCh. 5 - For each of the following pairs of atoms or ions,...Ch. 5 - For each of the following pairs of atoms or ions,...Ch. 5 - Predict the larger ion in each of the following...Ch. 5 - Prob. 36PCh. 5 - The first ionization energy of helium is...Ch. 5 - The energy needed to remove one electron from a...Ch. 5 - Without consulting any tables, arrange the...Ch. 5 - Both the electron affinity and the ionization...Ch. 5 - The cesium atom has the lowest ionization energy,...Ch. 5 - Until recently, it was thought that Ca was...Ch. 5 - In the hydrogen atom, the transition from the 2p...Ch. 5 - The energy needed to ionize an atom of element X...Ch. 5 - Suppose an atom in an excited state can return to...Ch. 5 - For the Li atom, the energy difference between the...Ch. 5 - How does the 3dxy orbital of an electron in O7+...Ch. 5 - The wave function of an electron in the lowest...Ch. 5 - An atom of sodium has the electron configuration...Ch. 5 - (a) The nitrogen atom has one electron in each of...Ch. 5 - Chromium(IV) oxide is used in making magnetic...Ch. 5 - Prob. 52APCh. 5 - Arrange the following seven atoms or ions in order...Ch. 5 - Which is higher, the third ionization energy of...Ch. 5 - The outermost electron in an alkali-metal atom is...Ch. 5 - In two-photon ionization spectroscopy, the...Ch. 5 - For the H atom, the transition from the 2p state...Ch. 5 - (a) Give the complete electron configuration...Ch. 5 - What experimental evidence does the periodic table...
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