Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantumnumbers: n, 1, and m.If the value of n =1The quantum number 1 can have values fromThe total number of orbitals possible at the n =1 energy level istoIf the value of 1= 0The quantum number mị can have values fromThe total number of orbitals possible at the 1= 0 sublevel isto

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Answered: Solution of the Schrödinger wave…

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter5: Electron Configurations And The Periodic Table

Section: Chapter Questions

Problem 135QRT

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Similar questions

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?
What experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?
6.96 When a helium atom absorbs light at 58.44 nm, an electron is promoted from the 1s orbital to a 2p orbital. Given that the ionization energy of (ground state) helium is 2372 kJ/ mol, find the longest wavelength of light that could eject an electron from the excited state helium atom.
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
6.32 What are the mathematical origins of quantum numbers?
What type of relationship (direct or inverse) e xists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?
Imagine a world in which the rule for the l quantum number is that values start with 1 and go up to n. The rules for the n and mi quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., n = 1 and n = 2).
According to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy, En, of an electron in a stable orbit of quantum number n is En = [Z2/n2] (2.179 1018 J) where Z is the atomic number. Calculate the ionization energy for the electron in a ground-state He+ ion.
Which of the following sets of quantum numbers correctly represents a 4p orbital? (a) n = 4, = 0, m = 1 (b) n = 4, = 1, m = 0 (c) n = 4, = 2, m = 1 (d) n = 4, = 1, m =2
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?
Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.
6.71 Several excited states of the neon atom are important in the operation of a helium-neon laser. In these excited states, one electron of the neon atom is promoted from the 2p level to a higher energy orbital. An excited neon atom with a 1s22s22p55s1 electron configuration can emit a photon with a wavelength of 3391 nm as it makes a transition to a lower energy state with a 1s22s22p54p1 electron configuration. Other transitions are also possible. If an excited neon atom with a 1s22s22p53p1 electron configuration makes a transition to a lower energy state with a 1s22s22p53p1 electron configuration, it emits a photon with a wavelength of 632.8 nm. Find the wavelength of the photon that would be emitted in a transition from the 1s22s22p54p1 electron configuration to the 1s22s22p53p1 electron configuration. (It should help if you start by drawing an energy-level diagram.)

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