Answered: 8. -/1 POINTS WAMODPHYS1 6.P.032. MY… | bartleby

Organic Chemistry: A Guided Inquiry

Organic Chemistry: A Guided Inquiry

2nd Edition

ISBN:9780618974122

Author:Andrei Straumanis

Publisher:Andrei Straumanis

ChapterL1: Infrared Spectroscopy

Section: Chapter Questions

Problem 6CTQ

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8.
-/1 POINTS
WAMODPHYS1 6.P.032.
MY NOTES
ASK YOUR TEACHER
The spring constant of a quantum harmonic oscillator in a potential well is 7.65 N/m. Determine the wavelength (in nm) of light the electron will emit as it jumps from
the n = 5 to n = 3 state.
nm

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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.)
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.)
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.
Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.
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.)
The Lyman series of spectral lines for the H atom, in the ultraviolet region, arises from transitions from higher levels to n = 1. Calculate the frequency and wavelength of the least energetic line in this series.
Draw, label, and explain the functions of the parts of a spectroscope.
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?
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.
Lasers are now used for the total or partial removal of skin tattoos. A laser with a wavelenth of 755 nm is used to remove tattoos in green or blue inks. (a) How much energy (in kJ/mol) is given off by the laser? (b) Compare the energy obtained in (a) with that given off by an x-ray (=1109m).
The maximum in the blackbody radiation intensity curve moves to shorter wavelength as temperature increases. The German physicist Wilhelm Wien demonstrated the relation to be max1/T . Later, Planck’s equation showed the maximum to be max=0.20hc/kt . In 1965, scientists researching problems in telecommunication discovered “background radiation” with maximum wavelength 1.05 mm (microwave region of the EM spectrum) throughout space. Estimate the temperature of space.
List some unexplainable phenomena from the classical science and describe what could not be explained about them at the time.

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