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.

Verified step by step guidance

1. Step 1: Understand that Moseley's law states that the square root of the frequency of the X-rays emitted by an element is directly proportional to the atomic number of the element. This relationship can be expressed as: √ν = a(Z - b), where ν is the frequency, Z is the atomic number, a and b are constants.
2. Step 2: Convert the given wavelengths to frequency using the formula ν = c/λ, where c is the speed of light and λ is the wavelength. Remember that the speed of light is approximately 3.00 x 10^8 m/s and you need to convert the wavelengths from picometers to meters.
3. Step 3: Plot the square root of the frequencies against the atomic numbers of the given elements. From this plot, determine the constants a and b in Moseley's law.
4. Step 4: Use the atomic number of iron (26) and the constants a and b determined in the previous step to calculate the frequency of the X-rays emitted by iron using Moseley's law.
5. Step 5: Convert the calculated frequency back to wavelength using the formula λ = c/ν. This will give you the predicted X-ray wavelength emitted by iron.

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element, defined as the number of protons in the nucleus of an atom. It determines the element's identity and its position in the periodic table. Moseley's work demonstrated that the atomic number, rather than atomic mass, is the correct basis for organizing the elements, as it correlates with the wavelengths of X-rays emitted by the elements.

X-ray Emission

X-ray emission occurs when high-energy electrons collide with atoms, causing the ejection of inner-shell electrons. This creates vacancies that are filled by electrons from higher energy levels, resulting in the release of energy in the form of X-rays. The wavelengths of these emitted X-rays are characteristic of the element and can be used to infer information about its atomic structure.

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. This relationship is crucial for predicting the X-ray wavelengths of elements based on their atomic numbers, as higher atomic numbers typically result in shorter wavelengths.