Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.6 - Electronic Structure of Atoms

Problema 37a

Capitolo 6, Problema 37a

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? a. from n = 4 to n = 2

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Identify the initial and final energy levels of the electron in the hydrogen atom. Here, the electron transitions from n = 4 (initial) to n = 2 (final).

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 = 4 to n = 2, it is transitioning from a higher energy level to a lower energy level.

Conclude that energy is emitted during this transition because the electron is moving to a lower energy state.

Use the Rydberg formula to calculate the energy of the emitted photon if needed: \( \Delta E = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_1 = 2 \), and \( n_2 = 4 \).

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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 (like n=4) have more energy than lower levels (like n=2). Understanding these energy levels is crucial for predicting whether energy is absorbed or emitted during electronic transitions.

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Hydrogenation Reactions

Photon Emission and Absorption

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

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Gamma Emission

Rydberg Formula

The Rydberg formula provides a mathematical relationship to calculate the wavelengths of the spectral lines in hydrogen. It is expressed as 1/λ = R(1/n1² - 1/n2²), where R is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the lower and higher energy levels, respectively. This formula helps quantify the energy changes during electronic transitions.

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Skeletal Formula

Pratica correlata

Domanda del libro di testo

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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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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Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? b. from an orbit of radius 2.12 Å to one of radius 8.46 Å

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

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a. Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 2 and when n = 6. Calculate the wavelength of the radiation released when an electron moves from n = 6 to n = 2.

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