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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 38a

Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 3

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Levels in Hydrogen

In a hydrogen atom, electrons occupy specific energy levels, denoted by quantum numbers (n). The energy associated with each level increases with n, meaning that higher levels are further from the nucleus and have more energy. Understanding these levels is crucial for determining whether energy is absorbed or emitted during electronic transitions.
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Absorption and Emission of Energy

When an electron transitions from a lower energy level (n = 2) to a higher energy level (n = 3), it must absorb energy, typically in the form of a photon. Conversely, when an electron falls from a higher level to a lower one, energy is emitted. This principle is fundamental in understanding how atoms interact with light and other forms of energy.
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Photon Energy and the Rydberg Formula

The energy of a photon is related to its frequency and wavelength, described by the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. The Rydberg formula can be used to calculate the wavelengths of emitted or absorbed light during electronic transitions in hydrogen, providing a quantitative understanding of these processes.
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Related Practice
Textbook Question

Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

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Textbook Question

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 3 to n = 2

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Textbook Question

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (b) from an orbit of radius 0.846 nm to one of radius 0.212 nm

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Textbook Question

(a) Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 3 and when n = 6. Calculate the wavelength of the radiation released when an electron moves from n = 6 to n = 3. when n = 6

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Textbook Question

The visible emission lines observed by Balmer all involved nf = 2. (a) Which of the following is the best explanation of why the lines with nf = 3 are not observed in the visible portion of the spectrum: (i) Transitions to nf = 3 are not allowed to happen, (ii) transitions to nf = 3 emit photons in the infrared portion of the spectrum, (iii) transitions to nf = 3 emit photons in the ultraviolet portion of the spectrum, or (iv) transitions to nf = 3 emit photons that are at exactly the same wavelengths as those to nf = 2.

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Textbook Question

The visible emission lines observed by Balmer all involved nf = 2. (b) Calculate the wavelengths of the first three lines in the Balmer series—those for which ni = 3, 4, and 5—and identify these lines in the emission spectrum shown in Figure 6.11.

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