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Ch.7 - Periodic Properties of the Elements
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 7, Problema 109a

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.

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1. The first step is to convert the wavelength from picometers (pm) to meters (m) since the standard unit of wavelength in the formula for frequency is meters. You can do this by multiplying the given wavelength by 1e-12.
2. Once you have the wavelength in meters, you can calculate the frequency using the formula for the speed of light, c = λν, where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength, and ν is the frequency. Rearranging the formula to solve for frequency gives ν = c/λ.
3. Substitute the speed of light and the wavelength (in meters) into the formula to calculate the frequency for each element.
4. Repeat these steps for each of the elements to find their respective frequencies.
5. Remember that the frequency will be in Hz (Hertz), which is equivalent to s^-1 (per second).

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Frequency and Wavelength Relationship

The frequency of electromagnetic radiation is inversely related to its wavelength, described by the equation c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in hertz (Hz). This relationship is fundamental in calculating the frequency of X-rays from their given wavelengths.
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Frequency-Wavelength Relationship

Units of Measurement

In the context of this question, it is crucial to convert the given wavelengths from picometers (pm) to meters (m) for accurate calculations. Since 1 pm equals 1 x 10^-12 meters, understanding unit conversion is essential for applying the frequency-wavelength relationship correctly.
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Units of Radiation Measurement

Electromagnetic Spectrum

X-rays are a form of electromagnetic radiation, which includes a range of wavelengths and frequencies. Understanding where X-rays fit within the electromagnetic spectrum helps contextualize their properties and applications, including their role in Moseley's work on atomic numbers and the study of atomic structure.
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Electromagnetic Spectrum
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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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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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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?

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