Ch.7 - Periodic Properties of the Elements

Brown - Chemistry: The Central Science 14th Edition

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

Brown 14th Edition

Ch.7 - Periodic Properties of the Elements

문제 109b,e

7장, 문제 109b,e

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (b) Plot the square root of n versus the atomic number of the element. What do you observe about the plot? (e) A particular element emits X rays with a wavelength of 98.0 pm. What element do you think it is?

검증된 단계별 안내

1. Moseley's law states that the frequency of the characteristic X-rays emitted by an element is proportional to the square of its atomic number (Z). The law can be written as: \(\nu = a(Z - b)^2\), where \(\nu\) is the frequency, \(Z\) is the atomic number, \(a\) and \(b\) are constants.

2. The frequency (\(\nu\)) and the wavelength (\(\lambda\)) of a wave are related by the equation \(\nu = c/\lambda\), where \(c\) is the speed of light. Therefore, we can rewrite Moseley's law in terms of wavelength: \(c/\lambda = a(Z - b)^2\).

3. From the given data, we can see that as the atomic number increases, the wavelength of the X-rays decreases. This is consistent with Moseley's law.

4. Given that the wavelength of the X-rays emitted by the unknown element is 98.0 pm, we can compare this value with the wavelengths of the known elements. The element with the wavelength closest to 98.0 pm is likely to be the unknown element.

5. By comparing the given wavelength of 98.0 pm with the provided data, we can see that it falls between the wavelengths for Zn (143.5 pm) and Zr (78.6 pm). Therefore, the unknown element is likely to be one of the elements in this range of the periodic table.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

12m

주요 개념

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

Atomic Number

The atomic number of an element is defined as the number of protons in its nucleus, which determines the element's identity and its position in the periodic table. Moseley's work demonstrated that the atomic number is a more fundamental property than atomic mass, as it correlates with the X-ray wavelengths emitted by elements when they are excited.

X-ray Emission

X-ray emission occurs when high-energy electrons collide with atoms, causing inner-shell electrons to be ejected and resulting in the transition of outer-shell electrons to lower energy levels. This transition releases energy in the form of X-rays, with specific wavelengths that are characteristic of each element, allowing for the identification of elements based on their emitted X-ray wavelengths.

Wavelength and Energy Relationship

The wavelength of electromagnetic radiation is inversely related to its energy, as described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Shorter wavelengths correspond to higher energy photons, which is crucial for understanding the X-ray emissions from elements and determining their atomic numbers based on the observed wavelengths.

관련 실천

교과서 질문

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (d) Use the result from part (b) to predict the X-ray wavelength emitted by iron.

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교과서 질문

One way to measure ionization energies is ultraviolet photoelectron spectroscopy (PES), a technique based on the photoelectric effect. (Section 6.2) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength 58.4 nm. (b) Write an equation that shows the process corresponding to the first ionization energy of Hg.

교과서 질문

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (e) A particular element emits X rays with a wavelength of 98.0 pm. What element do you think it is?

교과서 질문

We will see in Chapter 12 that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide, GaAs; gallium phosphide, GaP; cadmium sulfide, CdS; and cadmium selenide, CdSe. (b) Workers in the semiconductor industry refer to 'II–VI' and 'III–V' materials, using Roman numerals. Can you identify which compound semiconductors are II–VI and which are III–V? (c) Suggest other compositions of compound semiconductors based on the positions of their elements in the periodic table.

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교과서 질문

We will see in Chapter 12 that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide, GaAs; gallium phosphide, GaP; cadmium sulfide, CdS; and cadmium selenide, CdSe. (a) What is the relationship between the compound semiconductors' compositions and the positions of their elements on the periodic table relative to Si and Ge?

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교과서 질문

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (a) Calculate the frequency, n, of the X rays emitted by each of the elements, in Hz.

789

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