Chapter 6: Q2E (page 1247)

The positive muon $μ^{+}$ , an unstable particle, lives on average $2.20 \times 10^{- 6} s$ (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (b) What average distance, measured in the laboratory, does the particle move before decaying?

Short Answer

Expert verified

The total rest mass of the system is the sum of the relativistic masses of the particles, so in theory, a hot gas should have more mass than a cold one, but the difference is negligible.

Step by step solution

Concept of the relativistic mass

On average, the particles of a hot gas move faster than that of a cold gas. We know that the total rest mass of the system containing the gases is equal to the sum of the relativistic masses of the individual particles, and the relativistic mass is equal to $m_{r d} = γ m_{0}$ where $m_{0}$ is the rest mass and $γ'$ is the Lorentz factor. Since for $γ ≻ 1$ , then $m_{r d} ≻ m_{0}$ .

In practice, the values of the Lorentz factor for cold and hot gases are very nearly 1 since the particles move at a velocity much lower than the speed of light, so the difference between the masses of the system is negligible

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.

Short Answer

Step by step solution

Concept of the relativistic mass

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Electric Charge Field and Potential

Conservation of Energy and Momentum

Medical Physics

Turning Points in Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.