-The probability density plots of 1s and 2s orbitals are given in Fig. 1s 2s - The density of dots in a region represents the probability density of finding Electrons in the region. - On the basis of above diagram which of the following statements is incorrect? (A) 1s and 2s orbitals are spherical in shape. (B) The probability of finding the electron is maximum near the nucleus. (C) The probability of finding the electron at a given distance is equal in All directions. (D) The probability density of O electrons for 2s orbital decreases uniformly as

-The probability density plots of 1s and 2s orbitals are given in Fig. 1s 2s - The density of dots in a region represents the probability density of finding Electrons in the region. - On the basis of above diagram which of the following statements is incorrect? (A) 1s and 2s orbitals are spherical in shape. (B) The probability of finding the electron is maximum near the nucleus. (C) The probability of finding the electron at a given distance is equal in All directions. (D) The probability density of O electrons for 2s orbital decreases uniformly as

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

Chapter5: Quantum Mechanics And Atomic Structure

Section: Chapter Questions

Problem 6P: Using Table 5.2, write down the mathematical expression for the 2px wave function for an...

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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.)
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?
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.
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?
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.)
In a FranckHertz experiment on sodium atoms, the first excitation threshold occurs at 2.103 eV. Calculate the wavelength of emitted light expected just above this threshold. (Note: Sodium vapor lamps used in street lighting emit spectral lines with wavelengths 5891.8 and 5889.9 Å.)
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.
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.
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
(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.
(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 5.2) to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.
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.