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?

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

2. The frequency and wavelength of light are inversely proportional. This relationship is given by the equation: $\nu = c/\lambda$, where $\nu$ is the frequency, $c$ is the speed of light, and $\lambda$ is the wavelength.

3. From the given data, we can see that as the atomic number increases, the wavelength of the emitted 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. Looking at the given data, the element Zr has a wavelength of 78.6 pm and the element Sn has a wavelength of 49.1 pm. The wavelength of the unknown element (98.0 pm) falls between these two values, so the unknown element is likely to be one that has an atomic number between those of Zr and Sn.

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Key Concepts

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

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 unique X-ray emission patterns of each element.

X-ray Emission

X-ray emission occurs when electrons transition between energy levels in an atom, resulting in the release of energy in the form of X-rays. The wavelength of these X-rays is characteristic of the element, allowing scientists to identify elements based on their unique X-ray spectra.

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, which is crucial for understanding the X-ray emissions of elements and identifying them based on their emitted wavelengths.

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Frequency-Wavelength Relationship

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Textbook Question

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.

Textbook Question

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?

Textbook Question

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.

Textbook Question

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.

Textbook Question

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. (c) The kinetic energy of the emitted electrons is measured to be 1.72 × 10^-18 J. What is the first ionization energy of Hg, in kJ/mol?

Textbook Question

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. (d) Using Figure 7.10, determine which of the halogen elements has a first ionization energy closest to that of mercury.