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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.6 - Electronic Structure of AtomsProblem 37a,c
Chapter 6, Problem 37a,c

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 3 to n = 2 (c) an electron adds to the H+ ion and ends up in the n = 2 shell?

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Identify the initial and final energy levels of the electron in the hydrogen atom. In this case, the electron transitions from n = 3 to n = 2.
Recall that energy is emitted when an electron moves from a higher energy level to a lower energy level, and energy is absorbed when it moves from a lower energy level to a higher energy level.
Since the electron is moving from n = 3 (higher energy level) to n = 2 (lower energy level), energy will be emitted.
Use the Rydberg formula to calculate the energy change: \( \Delta E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_f \) is the final energy level, and \( n_i \) is the initial energy level.
Substitute the values \( n_i = 3 \) and \( n_f = 2 \) into the Rydberg formula to find the energy change, confirming that it is negative, indicating emission of energy.

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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 hydrogen, electrons occupy discrete energy levels, denoted by quantum numbers (n). The energy associated with each level increases with n, meaning that higher levels (larger n) have more energy. When an electron transitions between these levels, it either absorbs or emits energy, depending on whether it moves to a higher or lower energy level.

Photon Emission and Absorption

When an electron transitions from a higher energy level to a lower one, it emits energy in the form of a photon. Conversely, when it moves from a lower to a higher energy level, it absorbs a photon. The energy of the emitted or absorbed photon corresponds to the difference in energy between the two levels involved in the transition.

Calculating Energy Changes

The energy change associated with an electronic transition can be calculated using the formula ΔE = E_final - E_initial, where E is the energy of the respective levels. For hydrogen, the energy of each level can be determined using the Rydberg formula, which allows for the calculation of the energy of the photon emitted or absorbed during the transition.
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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

(b) Is this line in the visible region of the electromagnetic spectrum?

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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.

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Textbook Question

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

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Textbook Question

Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 3 (c) from the n = 9 to the n = 6 state.

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