Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

문제 42a

6장, 문제 42a

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.

검증된 단계별 안내

Identify the Lyman series in the context of the hydrogen atom's emission spectrum, where the final energy level (n_f) is 1.

Recall that the Lyman series involves electronic transitions from higher energy levels (n_i > 1) to the n_f = 1 level.

Use the Rydberg formula for hydrogen: \( \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant and \( n_i \) is the initial energy level.

Recognize that the Lyman series transitions result in the release of photons with wavelengths in the ultraviolet (UV) region of the electromagnetic spectrum.

Conclude that the Lyman series lines are observed in the ultraviolet region, as these transitions involve high energy changes.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Lyman Series

The Lyman series refers to a set of spectral lines corresponding to transitions of electrons in a hydrogen atom from higher energy levels (n ≥ 2) to the lowest energy level (n = 1). These transitions result in the emission of ultraviolet light, which is a key feature of hydrogen's emission spectrum.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves. The Lyman series specifically falls within the ultraviolet region of this spectrum.

Energy Level Transitions

Energy level transitions in an atom occur when an electron moves between different energy states. When an electron drops from a higher energy level to a lower one, it releases energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels, determining the wavelength and thus the position in the electromagnetic spectrum.

관련 실천

교과서 질문

One of the emission lines of the hydrogen atom has a wavelength of 94.974 nm. (a) In what region of the electromagnetic spectrum is this emission found?

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교과서 질문

One of the emission lines of the hydrogen atom has a wavelength of 94.974 nm. (b) Determine the initial and final values of n associated with this emission.

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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교과서 질문

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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교과서 질문

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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교과서 질문

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (b) Calculate the wavelengths of the first three lines in the Lyman series—those for which ni = 2, 3, and 4.

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