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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
6장, 문제 83c

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (c) When burned, a sample of an unknown substance is found to emit light of frequency 6.58 × 1014 s-1. Which of these elements is probably in the sample?

검증된 단계별 안내
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1. The problem provides the frequency of the light emitted by the unknown substance. However, the table provides the wavelengths of the light emitted by known substances. To compare these values, we need to convert the given frequency to wavelength. We can do this using the formula for the speed of light, which is \(c = \lambda \nu\), where \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(\nu\) is the frequency.
2. Rearrange the formula to solve for wavelength: \(\lambda = \frac{c}{\nu}\).
3. Substitute the given frequency and the speed of light (approximately \(3.00 \times 10^8\) m/s) into the formula to calculate the wavelength. Remember to convert the wavelength from meters to nanometers by multiplying by \(1 \times 10^9\).
4. Once you have the wavelength of the light emitted by the unknown substance, compare this value to the wavelengths given in the table.
5. The element in the table with a wavelength closest to the calculated wavelength is likely the element present in the unknown substance.

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주요 개념

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

Emission Spectra

Emission spectra are unique patterns of light emitted by elements when they are heated or energized. Each element emits light at specific wavelengths, which correspond to the energy transitions of electrons within the atoms. By analyzing these wavelengths, chemists can identify the presence of particular elements in a sample.
추천 영상:
가이드 코스
01:51
Emission Spectra

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This means that as the frequency of light increases, its wavelength decreases, and vice versa. Understanding this relationship is crucial for converting the given frequency of light emitted by the unknown substance into a wavelength for comparison with known emission wavelengths.
추천 영상:
가이드 코스
00:31
Frequency-Wavelength Relationship

Quantization of Energy Levels

In atoms, electrons occupy quantized energy levels, and transitions between these levels result in the emission or absorption of light at specific wavelengths. When an electron moves from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels. This principle underlies the characteristic wavelengths observed in the emission spectra of elements.
추천 영상:
가이드 코스
01:26
Nature of Energy
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교과서 질문

If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange (“flame test”). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (c) Calculate the energy gap between the excited and ground states for the calcium atom.

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교과서 질문

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (a) Determine which of these emissions occur in the ultraviolet part of the spectrum.

교과서 질문

If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange ('flame test'). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (b) What is the energy of 1.00 mol of these photons (a mole of photons is called an Einstein)?

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