Imagine an alternate universe where the quantum numbers for the hydrogen-like atom follow different rules. Inthis alternative universe, the m quantum number is only allowed to take zero or even numbers (ie. allowedquantum numbers are 0, +2, +4... but NOT +1). All other rules regarding the quantum numbers of thewavefunctions fo the hydrogen-like atom, including the maximum allowed values for quantum numbers I and m,are unchanged. All rules regarding filling orbitals with electrons, such as the Pauli exclusion principle, are alsounchanged. In this alternate universe, what elements would you predict to be noble gasses?In your work, clearly indicate a) how many distinct s, p and d orbitals there are in your alternate universe and b)what is the maximum number of electrons that can occupy the s, p and d sub levels.O H, Li, NaНе, Ве, ОO He, Ne, AlО Н, С, Са

The Pauli Exclusion Principle expresses that, in a particle or atom, no two electrons can have a…

Imagine an alternate universe where the quantum numbers for the hydrogen-like atom follow different rules. In this alternative universe, the m quantum number is only allowed to take zero or even numbers (ie. allowed quantum numbers are 0, +2, ±4... but NOT ±1). All other rules regarding the quantum numbers of the wavefunctions fo the hydrogen-like atom, including the maximum allowed values for quantum numbers l and m, are unchanged. All rules regarding filling orbitals with electrons, such as the Pauli exclusion principle, are also unchanged. In this alternate universe, what elements would you predict to be noble gasses? In your work, clearly indicate a) how many distinct s, p and d orbitals there are in your alternate universe and b) what is the maximum number of electrons that can occupy the s, p and d sub levels. O H, Li, Na О Не, Ве, О O He, Ne, Al О Не, С, Са

Imagine an alternate universe where the quantum numbers for the hydrogen-like atom follow different rules. In this alternative universe, the m quantum number is only allowed to take zero or even numbers (ie. allowed quantum numbers are 0, +2, ±4... but NOT ±1). All other rules regarding the quantum numbers of the wavefunctions fo the hydrogen-like atom, including the maximum allowed values for quantum numbers l and m, are unchanged. All rules regarding filling orbitals with electrons, such as the Pauli exclusion principle, are also unchanged. In this alternate universe, what elements would you predict to be noble gasses? In your work, clearly indicate a) how many distinct s, p and d orbitals there are in your alternate universe and b) what is the maximum number of electrons that can occupy the s, p and d sub levels. O H, Li, Na О Не, Ве, О O He, Ne, Al О Не, С, Са

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 59AP

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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.)
(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.
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?
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.
The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?
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?
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).
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?
What are the values of E, L, and Lz for an F8+ atom whose electron has the following wavefunctions, listed as n,l,ml? a 1,0,0 b 3,2,2c 2,1,1d 9,6,3.
Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator wavefunction that has a very high value of n. Explain how this is consistent with the correspondence principle.
A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.
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.