1.39 Evaluate the probability of findingof a hydrogen 1s-orbital at a distance 0.55a0 from the nucleusrelative to finding it in the same small region located at the nucleus.an electron in a small region

The normalized probability of finding an electron at a distance R from the center is given below.

Answered: 1.39 Evaluate the probability of…

Chemistry: Principles and Practice

3rd Edition

ISBN:9780534420123

Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer

Chapter7: Electronic Structure

Section: Chapter Questions

Problem 7.60QE

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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.)
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 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.
State how many radial, angular, and total nodes are in each of the following hydrogen-like wavefunctions. a 2s b 3s c 3p d 4f e 6g f 7s
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 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?
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.)
Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 nm. What is the initial excited state for the electron (n = ?)?
How is the Bohr theory of the hydrogen atom inconsistent with the uncertainty principle? In fact, it was this inconsistency, along with the theorys limited application to non-hydrogen-like systems, that limited Bohrs theory.
(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.
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?

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1.39 Evaluate the probability of finding of a hydrogen 1s-orbital at a distance 0.55a0 from the nucleus relative to finding it in the same small region located at the nucleus. an electron in a small region