Concept explainers
When one of helium’s electrons is removed, the resulting species is the helium ion. He+. The He+ ion contains only one electron and is therefore a “hydrogen-like ion.” Calculate the wavelengths, in increasing order, of the first four transitions in the Balmer series of the He+ ion. Compare these wavelengths with the same transitions in an H atom. Comment on the differences. (The Rydberg constant for He is 4.39 × 107 m−1.)
Interpretation:
The wavelengths in the increasing order of the first four transitions in the Balmer series of the
Concept Introduction:
Absorption refers to how much light can be taken in by the material being measured.
When electromagnetic radiation interacts with matter, atoms and molecules may absorb energy and reach to a higher energy state. With higher energy, these are in an unstable state. For returning to their normal (more stable, lower energy) energy state, the atoms and molecules emit radiations in various regions of the electromagnetic spectrum. The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum.
In 1885, Johann Balmer developed a simple equation which could be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen. Johannes Rydberg developed Balmer’s equation further, giving an equation which could calculate the visible wavelengths and also those of all hydrogen’s spectral lines.
This equation is known as the Rydberg equation. Here,
To find: Calculate the wavelengths in the increasing order of the first four transitions in the Balmer series of the
Answer to Problem 3.133QP
The wavelengths of the first four transitions in the Balmer series of the
Explanation of Solution
When one of helium’s electrons is removed, the resulting species is the helium ion,
Here, the Rydberg constant for
For the transition
The negative sign indicates that the emission of light occurs. Wavelengths are always positive signs. Here,
For the transition
For the transition
For the transition
The Rydberg constant for
The negative sign indicates that the emission of light occurs. Wavelengths are always positive signs. Here,
For the transition
For the transition
For the transition
All the Balmer transitions for
The wavelengths in the increasing order of the first four transitions in the Balmer series of the
Want to see more full solutions like this?
Chapter 3 Solutions
EBK CHEMISTRY: ATOMS FIRST
- This laser emits green light with a wavelength of 533 nm. (a) What is the energy, in joules, of one photon of light at this wavelength? (b) If a particular laser produces 1.00 watt (W) of power (1 W = 1 J/s), how many photons are produced each second by the laser?arrow_forwardA baseball weighs 142 g. A professional pitcher throws a fast ball at a speed of 100 mph and a curve ball at 80 mph. What wavelengths are associated with the motions of the baseball? If the uncertainty in the position of the ball is 12 wavelength, which ball (fast ball or curve) has a more precisely known position? Can the uncertainty in the position of a curve ball be used to explain why batters frequently miss it?arrow_forwardShow that the value of the Rydberg constant per photon, 2.179 1018 J, is equivalent to 1312 kJ/mol photons.arrow_forward
- 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.arrow_forwardInvestigating 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.arrow_forward
- Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningOrganic Chemistry: A Guided InquiryChemistryISBN:9780618974122Author:Andrei StraumanisPublisher:Cengage Learning
- General Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning