Which of the following statements is a valid conclusion from the Heisenberg uncertainty principle? The square of the wave function is proportional to the probability of finding a particle in space. O The act of measuring a particle's position changes its momentum, and vice versa. O Particles can exhibit wavelike behavior. O An electron in a 2p orbital is always closer to the nucleus than an electron in a 3p orbital. O The orbits proposed by Bohr's model of the atom are correct.

Which of the following statements is a valid conclusion from the Heisenberg uncertainty principle? The square of the wave function is proportional to the probability of finding a particle in space. O The act of measuring a particle's position changes its momentum, and vice versa. O Particles can exhibit wavelike behavior. O An electron in a 2p orbital is always closer to the nucleus than an electron in a 3p orbital. O The orbits proposed by Bohr's model of the atom are correct.

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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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?
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?
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 cesium atom has the lowest ionization energy, 375.7kJmol1 , of all the neutral atoms in the periodic table. What is the longest wavelength of light that could ionize a cesium atom? In which region of the electromagnetic spectrum does this light fall?
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.)
Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?
6.32 What are the mathematical origins of quantum numbers?
• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.
The wave function for the 2pz, orbital in the hydrogen atom is 2pl=142(za0)3/2e/2cos where a0 is the value for the radius of the first Bohr orbit in meters (5.29 | 1011), is Z(r/a0), r is the value for the distance from the nucleus in meters, and is an angle. Calculate the value of 2pz2 at r = a0 for = 0 (z axis) and for = 90 (xy plane).