Is Add-ons Help Last edit was made 3 hours ago by Courtney Redilla- Arial- BIUA.1413. The color orange within the visible light spectrum has a wavelength of about 620 nm. Whatis the frequency of orange light?4. The red light from a helium-neon laser has a wavelength of 633 nm. What is the energy ofone photon? For one mole of these photons?rr

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Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.14E

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Similar questions

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.)
Suppose an atom in an excited state can return to the ground state in two steps. It first falls to an intermediate state, emitting radiation of wavelength 1 , and then to the ground state, emitting radiation of wavelength 2 . The same atom can also return to the ground state in one step, with the emission of radiation of wavelength . How are 1,2, and related? How are the frequencies of the three radiations related?
Explain why the wave model for radiation cannot account for the photoelectric effect.
Electron microscopes operate on the fact that electrons act as waves. A typical electron kinetic energy is 100keV 1eV=1.6021019J. What is the wavelength of such an electron? Ignore relativistic effects.
Why isnt the electron configuration of beryllium, given as 1s22s2, considered a violation of the Pauli principle? Hint: See example 12.6.
Ultrasonic waves have frequencies too high to be detected by the human ear, but they can be produced and detected by vibrating crystals. Calculate the wavelength of an ultrasonic wave of frequency 5.0104s1 that is propagating through a sample of water at a speed of 1.5103ms1 . Explain why ultrasound can be used to probe the size and position of the fetus inside the mother’s abdomen. Could audible sound with a frequency of 8000s1 be used for this purpose?
Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene (see Example 4.7) and the n=2 wave function for the weakest bound electron, calculate the probability of finding the electron in an 0.1 interval centered midway between the two inner carbon atoms (that is, the center is at x=2.11 , so this interval is from x1=2.06 to x2=2.16 ). Then calculate the probability of finding the electron in an 0.1 interval centered midway between an end carbon atom and the carbon atom that is double-bonded to it in the Lewis dot structure. (You may calculate the appropriate integrals or estimate the relevant areas under the curve graphically.) Then recalculate the probabilities by approximating the integral as |( x 0)|2x , where x0 is evaluated in the middle of the range from x1 to x2 . Finally, explain why you can’t approximate the integral needed for Problem 37(a) in this way.
The speed of sound in dry air at 20°C is 343.5ms1 , and the frequency of the sound from the middle C note on a piano is 261.6s1 (according to the American standard pitch scale). Calculate the wavelength of this sound and the time it will take to travel 30.0 m across a concert hall.
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.)
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?
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.

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