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 A1, and then to the ground state, emitting radiation of wavelength A2. The same atom can also return to the ground state in one step, with the emission of radiation of wavelength A. How are d1, d 2, and A related? How are the frequencies of the three radiations related?

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 A1, and then to the ground state, emitting radiation of wavelength A2. The same atom can also return to the ground state in one step, with the emission of radiation of wavelength A. How are d1, d 2, and A related? How are the frequencies of the three radiations related?

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 45AP: Suppose an atom in an excited state can return to the ground state in two steps. It first falls to...

See similar textbooks

Similar questions

6.9 If a string of decorative lights includes bulbs with wave-lengths of 480, 580, and 700 mm, what are the frequencies of the lights? Use Figure 6.6 to determine which colors are in the set.
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.)
Ozone in the stratosphere absorbs ultraviolet light of wavelengths shorter than 320 nm, thus filtering out the most energetic radiation from sunlight. During this absorption, an ozone molecule absorbs a photon, which breaks an oxygen-oxygen bond, yielding an oxygen molecule and an oxygen atom: O3(g)+hvO2(g)+O(g) (Here, hv denotes a photon.) Suppose a flask of ozone is irradiated with a pulse of UV light of wavelength 275 nm. Assuming that each photon of this pulse that is absorbed breaks up one ozone molecule, calculate the energy absorbed per mole of O2 produced, giving the answer in kJ/mol.
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?
The figure below represents part of the emission spectrum for a one-electron ion in lhe gas phase. All the lines result from electronic transitions from excited states to the n = 3 state. (See Exercise 160.) a. What electronic transitions correspond to lines A and B? b. If the wavelength of line B is 142.5 nm, calculate the wavelength of line A.
Consider only the transitions involving the first four energy levels for a hydrogen atom: a. How many emissions are possible for an electron in the n = 4 level as it goes to the ground state? b. Which electronic transition is the lowest energy? c. Which electronic transition corresponds to the shortest wavelength emission?
What type of relationship (direct or inverse) e xists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?
What are quantum numbers? What information do we get from the quantum numbers n, l, and ml? We define a spin quantum number (ms), but do we know that an electron literally spins?
Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.
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?
Photons are emitted in the Lyman series as hydrogen atoms undergo transitions from various excited states to the ground state. If ground-state He+ are present in the same gas (near stars, for example), can they absorb these photons? Explain.