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

Problem 89a

Chapter 6, Problem 89a

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (a) What is the end result of this transition?

Verified step by step guidance

Identify the initial and final energy levels of the electron. In this case, the electron transitions from the initial level n = 1.

Recognize that the final energy level n is not specified in the problem. To proceed, you would need the correct final energy level.

Understand that the energy difference between these levels determines the energy of the photon involved in the transition. The energy can be calculated using the formula: \( E = E_f - E_i \), where \( E_i \) and \( E_f \) are the initial and final energy states of the electron.

Recall that the energy levels of a hydrogen atom are given by the formula: \( E_n = -\frac{13.6 \text{ eV}}{n^2} \), where n is the principal quantum number.

If the final energy level n were known, you could calculate the energy of the photon emitted or absorbed during this transition using the difference in energy levels formula and then determine whether the electron absorbs or emits a photon.

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Key Concepts

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

Quantum Energy Levels

In quantum mechanics, electrons in an atom occupy discrete energy levels, denoted by quantum numbers (n). For hydrogen, these levels are quantized, meaning an electron can only exist in specific states. The transition from a lower energy level (n=1) to a higher one (n=2, for example) involves the absorption of energy, typically in the form of a photon.

Photon Absorption

When an electron transitions from a lower to a higher energy level, it absorbs a photon whose energy matches the difference between the two levels. The energy of the photon is given by the equation E = hf, where E is energy, h is Planck's constant, and f is the frequency of the photon. This process is fundamental in understanding how atoms interact with light.

Excited State

An excited state refers to an electron configuration where an electron has absorbed energy and moved to a higher energy level than its ground state. In the case of hydrogen, when the electron transitions from n=1 to n=2, it is in an excited state. This state is typically unstable, and the electron will eventually return to the ground state, often releasing energy in the form of light.

Related Practice

Textbook Question

In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled 'n0' corresponds to light with a wavelength of 542 nm. (a) What is the value of n0 in s - 1?

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Textbook Question

In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter, arriving nearly five years later in July of 2016. The distance between the two planets varies depending on where each planet is in its orbit, but at the closest, the distance between Jupiter and Earth is 391 million miles. What is the minimum amount of time it takes for a transmitted signal from Juno to reach the Earth?

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Textbook Question

The human retina has three types of receptor cones, each sensitive to a different range of wavelengths of visible light, as shown in this figure (the colors are merely to differentiate the three curves from one another; they do not indicate the actual colors represented by each curve):

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Textbook Question

The series of emission lines of the hydrogen atom for which nf = 3 is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed.

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Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (b) What is the wavelength of light that must be absorbed to accomplish this process?

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