Chapter 7: Problem 28
Explain how astronomers are able to tell which elements are present in distant stars by analyzing the electromagnetic radiation emitted by the stars.
Chapter 7: Problem 28
Explain how astronomers are able to tell which elements are present in distant stars by analyzing the electromagnetic radiation emitted by the stars.
All the tools & learning materials you need for study success - in one app.
Get started for freeThe blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a frequency of about \(7.5 \times 10^{14} \mathrm{~Hz}\). (a) Calculate the wavelength, in \(\mathrm{nm}\), associated with this radiation, and (b) calculate the energy, in joules, of a single photon associated with this frequency.
The sun is surrounded by a white circle of gaseous material called the corona, which becomes visible during a total eclipse of the sun. The temperature of the corona is in the millions of degrees Celsius, which is high enough to break up molecules and remove some or all of the electrons from atoms. One way astronomers have been able to estimate the temperature of the corona is by studying the emission lines of ions of certain elements. For example, the emission spectrum of \(\mathrm{Fe}^{14+}\) ions has been recorded and analyzed. Knowing that it takes \(3.5 \times 10^{4} \mathrm{~kJ} / \mathrm{mol}\) to convert \(\mathrm{Fe}^{13+}\) to \(\mathrm{Fe}^{14+},\) estimate the temperature of the sun's corona.
An electron in an excited state in a hydrogen atom can return to the ground state in two different ways: (a) via a direct transition in which a photon of wavelength \(\lambda_{1}\) is emitted and (b) via an intermediate excited state reached by the emission of a photon of wavelength \(\lambda_{2}\). This intermediate excited state then decays to the ground state by emitting another photon of wavelength \(\lambda_{3}\). Derive an equation that relates \(\lambda_{1}\) to \(\lambda_{2}\) and \(\lambda_{3}\)
Discuss the similarities and differences between a \(1 s\) and a \(2 s\) orbital.
Which of the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) determine (a) the energy of an electron in a hydrogen atom and in a many- electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?
What do you think about this solution?
We value your feedback to improve our textbook solutions.