Chapter 4: Q22E (page 135)

Roughly speaking for what range of wavelengths would we need to treat an electron relativistically, and what would be the corresponding range of accelerating potentials? Explain your assumptions.

Short Answer

Expert verified

Rane of Wavelength and Range of Accelerating potentials:

$λ \leq 2.43 \times 10^{-11} m, and V \geq 2.556 k eV$

Step by step solution

Step 1:Concept Introduction

The wavelength of any moving charged particle is given by the,

$λ = \frac{h}{\sqrt{2mqV}}$ …………………..(1)

Where m, q, and V are the mass, charge, and applied potential difference.

Step 2:Formula.

$\begin{matrix} λ = \frac{h}{p} = \frac{h}{m_{e} v} \\ λ = \frac{6.63 \times 10^{-34} J \cdot s}{(9.1 \times 10^{-31} kg) \times (3 \times 10^{7} m/s)} \\ λ = 2.43 \times 10^{-11} m \end{matrix}$

Relativistic Treatment.

Relativistic treatment is required for wavelengths equal to or smaller than this value.

$\begin{matrix} V = \frac{h^{2}}{{2m}_{e} {qλ}^{2}} \\ V = \frac{{(6.63 \times 10^{-34} J \cdot s)}^{2}}{2 \times (9.1 \times 10^{-31} kg) \times (1.6 \times 10^{-19} C) \times {(2.43 \times 10^{-11} m)}^{2}} \\ V = 2.556 keV \end{matrix}$

Relativistic therapy will be required if the potential is equal to or greater than this value.

$λ \leq 2.43 \times 10^{-11} m, and V \geq 2.556 k eV$

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.

Roughly speaking for what range of wavelengths would we need to treat an electron relativistically, and what would be the corresponding range of accelerating potentials? Explain your assumptions.

Short Answer

Step by step solution

Step 1:Concept Introduction

Step 2:Formula.

Relativistic Treatment.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Astrophysics

Physical Quantities And Units

Electromagnetism

Torque and Rotational Motion

Mechanics and Materials

Study anywhere. Anytime. Across all devices.