Chapter 36: Q. 38 (page 1060)

At what speed, as a fraction of $c$ , must an electron move so that its total energy is $10 %$ more than its rest mass energy?

Short Answer

Expert verified

$v = 1.24 \times 10^{8} m / s$

Step by step solution

Given Information

We have given that, $c = 3 \times 10^{8} m / s$

Total energy is $10 %$ more.

Simplify

Given values are: $c = 3 \times 10^{8} m / s$ and total energy is $10 %$ more.

To find the speed $v$ , we use the below given formula.

role="math" localid="1649826808978" $\frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = m c^{2} + 10 % of m c^{2}$

Now, put the given values in the above formula to find the speed.

$\frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = m c^{2} + 0.1 \times m c^{2} \frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = 1.1 m c^{2} \frac{1}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = 1.1 \sqrt{(1 - \frac{v^{2}}{c^{2}})} = \frac{1}{1.1} 1 - \frac{v^{2}}{c^{2}} = \frac{1}{1.21} \frac{v^{2}}{c^{2}} = \frac{0.21}{1.21} v^{2} = c^{2} \cdot \frac{21}{121} v = c \cdot \sqrt{\frac{21}{121}} v = 1.24 \times 10^{8} m / s$

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.

At what speed, as a fraction of $c$ , must an electron move so that its total energy is $10 %$ more than its rest mass energy?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Atoms and Radioactivity

Magnetism and Electromagnetic Induction

Solid State Physics

Magnetism

Oscillations

Study anywhere. Anytime. Across all devices.

At what speed, as a fraction of c, must an electron move so that its total energy is10% more than its rest mass energy?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Atoms and Radioactivity

Magnetism and Electromagnetic Induction

Solid State Physics

Magnetism

Oscillations

Study anywhere. Anytime. Across all devices.

At what speed, as a fraction of $c$ , must an electron move so that its total energy is $10 %$ more than its rest mass energy?