This energy diagram shows the allowed energy levels of an electron in a certain atom. (Note: the SI prefix 'zepto' means 10 any SI prefix in the ALEKS Data tab.) -21 '. You can find the meaning of 1400 1200 1000 800 energy (z) 600- -B 400 -A 200 Use this diagram to complete the table below. What is the energy of the electron in the ground state? What is the energy of the electron in the first excited state? If the electron makes the transition shown by the red arrow, from A to C, will a photon be absorbed or emitted? O absorbed emitted Calculate the wavelength of the photon that would be absorbed or emitted. Round your answer to 3 significant digits. I nm O o

This energy diagram shows the allowed energy levels of an electron in a certain atom. (Note: the SI prefix 'zepto' means 10 any SI prefix in the ALEKS Data tab.) -21 '. You can find the meaning of 1400 1200 1000 800 energy (z) 600- -B 400 -A 200 Use this diagram to complete the table below. What is the energy of the electron in the ground state? What is the energy of the electron in the first excited state? If the electron makes the transition shown by the red arrow, from A to C, will a photon be absorbed or emitted? O absorbed emitted Calculate the wavelength of the photon that would be absorbed or emitted. Round your answer to 3 significant digits. I nm O o

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter4: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 40P: When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid....

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For the Li atom, the energy difference between the ground state and the first excited state, in which the outermost electron is in a 2p orbital, is 2.961019J . In the Li2+ ion, the energy difference between the 2s and 2p levels is less than 0.00002 of this value. Explain this observation.
Photoelectron spectra were acquired from a sample of gaseous O2 using X-ray radiation with wavelength 0.99 nm and energy 1253.6 eV. The spectrum contained a large peak for photoelectrons with speed of 1.57107ms1 . Calculate the ionization energy of these electrons. Identify the orbital from which they were most likely emitted.
Quantum mechanics predicts that the energy of the ground state of the H atom is 13.6eV . Insight into the magnitude of this quantity is gained by considering several methods by which it can be measured. (a) Calculate the longest wavelength of light that will ionize H atoms in their ground state. (b) Assume the atom is ionized by collision with an electron that transfers all its kinetic energy to the atom in the ionization process. Calculate the speed of the electron before the collision. Express your answer in meters per second (ms1) and miles per hour (milesh1) . (c) Calculate the temperature required to ionize a H atom in its ground state by thermal excitation. (Hint: Recall the criterion for thermal excitation of an oscillator in Planck’s theory of blackbody radiation is that hvkBT .)
Consider the representations of the p and d atomic orbitals in Figs. 2-15 and 2- 17. What do the + and signs indicate?
(a) The nitrogen atom has one electron in each of the 2px , 2py , and 2pz orbitals. By using the form of the angular wave functions, show that the total electron density, 2(2px)+2(2py)+2(2pz) , is spherically symmetric (that is, it is independent of the angles and ). The neon atom, which has two electrons in each 2p orbital, is also spherically symmetric. (b) The same result as in part (a) applies to d orbitals, thus a filled or half-filled subshell of d orbitals is spherically symmetric. Identify the spherically symmetric atoms or ions among the following: F , Na, Si, S2,Ar+ , Ni, Cu, Mo, Rh, Sb, W, Au.
Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)
The following is an energy-level diagram for electronic transitions in the Bohr hydrogen atom. a. Explain why the energy levels get closer together as they increase. Provide mathematical support for this. b. Verify that the colors given in the diagram are correct. Provide mathematical support.
Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)
Consider the orbitals shown here in outline. (a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)? (b) How many orbitals of type (x) are found in a shell with n=2? How many of type (y)? How many of type (z)? (c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n=4, of an orbital of type (y) in a shell with n=2. Of an orbital of type (z) in a shell with n=3. (d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)? (e) What are the possible I and ml values for an orbital of type (x)? Of type (y)? Of type (z)?
Sketch the major features (number of peaks and relative intensities for the peaks) of the expected photoelectron spectrum for atoms of nitrogen.
The helium ion He+ is a one-electron system whose wave functions and energy levels are obtained from those for H by changing the atomic number to Z=2 . Calculate the average distance of the electron from the nucleus in the 2s orbital and in the 2p orbital. Compare your results with those in Problem 11 and explain the difference.
The figure below represents part of the emission spectrum for a one-electron ion in lhe gas phase. All the lines result from electronic transitions from excited states to the n = 3 state. (See Exercise 160.) a. What electronic transitions correspond to lines A and B? b. If the wavelength of line B is 142.5 nm, calculate the wavelength of line A.