6. Determine the ionization energy for the hydrogen atom. The ionization energy is the energynecessary to take an electron from its most stable state (n, = 1 for hydrogen), to a state infi-nitely far from the nucleus. Use Equation 3 to make the calculation. What is n? Show yourwork.he hckHEquation 3: AE2.n

Applying Bohr’s equation for the energy levels of hydrogen atom, the change in energy when an…

Answered: 6. Determine the ionization energy for…

Introductory Chemistry: An Active Learning Approach

6th Edition

ISBN:9781305079250

Author:Mark S. Cracolice, Ed Peters

Publisher:Mark S. Cracolice, Ed Peters

Chapter11: Atomic Theory :the Quantum Model Of The Atom

Section: Chapter Questions

Problem 109E

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The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr’s quantization of angular momentum to the revolution of Earth (mass6.01024kg) , which moves with a speed of 3.0104ms1 in a circular orbit (radius1.51011m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earthsun system. What would be the effect of an increase in n by 1?
The outermost electron in an alkali-metal atom is sometimes described as resembling an electron in the corresponding state of a one-electron atom. Compare the first ionization energy of lithium with the binding energy of a 2s electron in a one-electron atom that has nuclear charge Zeff , and determine the value of Zeff that is necessary for the two energies to agree. Repeat the calculation for the 3s electron of sodium and the 4s electron of potassium.
The ionization of the hydrogen atom can be calculated from Bohr's equation for the electron energy. E = (NARhc)(Z2/n2) where NARhc =1312 kJ/mol and Z is the atomic number. Let us use this approach to calculate a possible ionization energy for helium. First, assume the electrons of the He experience the full 2+ nuclear charge. This gives us the upper limit for the ionization energy. Next, assume one electron of He completely screens the nuclear charge from the other electrons, so Z = 1. This gives us a lower limit to the ionization energy. Compare these calculated values for the upper and lower limits to the experimental value of 2372.3 kJ/mol. What does this tell us about the ability of one electron to screen the nuclear charge?
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.
Consider the representations of the p and d atomic orbitals in Figs. 2-15 and 2- 17. What do the + and signs indicate?
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.
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.)
Use the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?
When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800 nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge L, and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length L in this simple model.
Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.
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)?
Suppose that the spin quantum number did not exist, and therefore only one electron could occupy each orbital of a many-electron atom. Give the atomic numbers of the first three noble-gas atoms in this case.

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