Ch.6 - Electronic Structure of Atoms

Problem 38a,c

Chapter 6, Problem 38a,c

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.

Verified step by step guidance

Identify the initial and final energy levels of the electron in the hydrogen atom. Here, the electron transitions from n = 2 to n = 3.

Recall that when an electron moves to a higher energy level (higher n value), it absorbs energy. Conversely, when it moves to a lower energy level, it emits energy.

Since the electron is moving from n = 2 to n = 3, it is transitioning to a higher energy level.

Conclude that energy is absorbed during this transition because the electron is moving to a higher energy state.

Remember that the energy difference between levels can be calculated using the Rydberg formula, but the key concept here is the direction of the transition (lower to higher energy level).

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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.

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.

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 (c) an electron adds to the H⁺ ion and ends up in the n = 2 shell?

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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.

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Textbook Question

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

Textbook Question

Consider a transition of the electron in the hydrogen atom from n = 8 to n = 3. (b) Will the light be absorbed or emitted?

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