1. Calculate the expectation value for the potential energy of the hydrogen atom with the electron in the 1s orbital. Compare your result with the total energy and calculate the expectation value of the electron's kinetic energy in this state. 2. (a) Calculate the probability that the Is electron for hydrogen will be found between ra, and r= 2ao. (b) Calculate the probability of finding the electron, still in the Is state, outside a sphere of radius 2.500. 3. Calculate the expectation value of the radius, (r), at which you would find the electron if the H atom wave function is a) w200, and b) 211. I

1. Calculate the expectation value for the potential energy of the hydrogen atom with the electron in the 1s orbital. Compare your result with the total energy and calculate the expectation value of the electron's kinetic energy in this state. 2. (a) Calculate the probability that the Is electron for hydrogen will be found between ra, and r= 2ao. (b) Calculate the probability of finding the electron, still in the Is state, outside a sphere of radius 2.500. 3. Calculate the expectation value of the radius, (r), at which you would find the electron if the H atom wave function is a) w200, and b) 211. I

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...

See similar textbooks

Similar questions

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?
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?
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.)
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.
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.)
Calculate the energies of an electron in the fourth, fifth, and sixth energy levels of the Bohr hydrogen atom.
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.
The energy needed to ionize an atom of element X when it is in its most stable state is 500kJmol1 . However, if an atom of X is in its lowest excited state, only 120kJmol1 is needed to ionize it. What is the wavelength of the radiation emitted when an atom of X undergoes a transition from the lowest excited state to the ground state?
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?
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
Defend and criticize Bohrs model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?