A Ka x ray emitted from a sample has an energy of 7.46 keV. Of which element is the sample made?

Name: Problem 36, Chapter 41: University Physics with Modern Physics
Uploaded: 2021-02-16T21:24:42-08:00
Duration: 3 min 6 s
Channel: Nathan Silvano
Description: A Ka x ray emitted from a sample has an energy of 7.46 keV. Of which element is the sample made?

step 1 Okay, so we know in this problem that k -alpha x -ray was emitted with an energy, let's put here

A Ka x ray emitted from a sample has an energy of 7.46 keV....

Key Concepts

Electron Transitions in Atoms

Electron transitions from one energy level to another within an atom release or absorb discrete amounts of energy, which manifest as photons of specific energies. In the context of x-ray emission, a transition typically occurs when an electron from a higher shell (such as the L shell) fills a vacancy in the innermost K shell, releasing a photon in the x-ray region. Understanding these transitions helps explain why the x-ray energies are quantized and characteristic of each element.

Characteristic X-Ray Emission

This concept encompasses the idea that each element emits x-rays at characteristic energies when its inner-shell electrons are removed and electrons from higher-energy shells fill the vacancies. The energies of these x-rays are unique to the element, serving as its spectral fingerprint. This principle is widely used in x-ray spectroscopy to identify the elemental composition of a sample without the need for extensive sample preparation.

Moseley’s Law

Moseley’s Law establishes a quantitative relationship between the x-ray emission energies and the atomic number of the corresponding element. Specifically, it shows that the square root of the frequency of the emitted x-ray is proportional to the atomic number minus a screening constant. This law provides a method to determine the atomic number (and thereby the identity) of an element by measuring the energy of its characteristic x-ray lines.

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