Chapter 10: Problem 34

Describe how the Bohr model may be used to account for characteristic x-ray spectra in heavy atoms.

Short Answer

Expert verified

Based on the given solution, provide a short answer for how the Bohr model accounts for characteristic x-ray spectra in heavy atoms. The Bohr model accounts for characteristic x-ray spectra in heavy atoms through its quantized energy levels. When an electron from a higher orbit fills a vacancy in a lower orbit, the energy difference between the two orbits results in the emission of a photon (x-ray) with a specific energy. This unique energy signature forms the characteristic x-ray spectrum for that heavy atom.

Step by step solution

1. Define the Bohr model and its main properties

The Bohr model, developed by Niels Bohr in 1913, describes an isolated atom as consisting of a positively charged nucleus surrounded by negatively charged electrons orbiting in discrete orbits. The electrons are assumed to follow circular orbits, and their orbits are quantized, meaning they can only occupy particular energy levels.

2. Importance of quantized energy levels

In the Bohr model, electrons can only exist in certain orbits with specific energy levels, described by the principal quantum number n. These quantized energy levels are essential because they allow for the unique energy signatures known as characteristic x-ray spectra.

3. Explain the generation of characteristic x-rays

Characteristic x-rays are generated when an electron from the inner orbit (closer to the nucleus) is removed and an electron from a higher orbit "jumps" to fill the vacancy in the lower orbit. Since the energy levels are quantized, this electron transition results in the emission of a photon (x-ray) with a specific energy equal to the energy difference between the two orbits involved.

4. Relevance of Bohr model to heavy atoms

The Bohr model is especially useful for heavy atoms because relativistic effects become increasingly important. The mass of an electron in motion is higher than its rest mass, affecting the energy levels and electromagnetic radiation emitted. This model is suitable for providing a simple, albeit limited, understanding of characteristic x-ray spectra for heavier elements.

5. Example of Bohr Model accounting for characteristic x-ray spectra

Let's consider an example in which an electron from the M-shell (n=3) fills a vacancy in the K-shell (n=1) of a heavy atom. The energy difference between these shells is given by the Rydberg formula: ΔE = -13.6 Z^2(1/n_final^2 - 1/n_initial^2)eV where ΔE is the energy difference, Z is the atomic number, n_final and n_initial are the principal quantum numbers of the final and initial orbits, respectively. Using the Bohr model and this formula, we can calculate the energy of the emitted x-ray photon as the electron transition takes place. In this example, the energy of the emitted x-ray will be unique to that specific transition, and it will be part of the characteristic x-ray spectrum of that heavy atom.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Describe how the Bohr model may be used to account for characteristic x-ray spectra in heavy atoms.

Short Answer

Step by step solution

1. Define the Bohr model and its main properties

2. Importance of quantized energy levels

3. Explain the generation of characteristic x-rays

4. Relevance of Bohr model to heavy atoms

5. Example of Bohr Model accounting for characteristic x-ray spectra

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Magnetism and Electromagnetic Induction

Force

Rotational Dynamics

Energy Physics

Electromagnetism

Study anywhere. Anytime. Across all devices.