Chapter 36: Q. 57 (page 1061)

Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of $0.99 c$ ?

Short Answer

Expert verified

The potential difference required is $3.12 \times 10^{6} V$ .

Step by step solution

Given Information

We have given that, speed $v = 0.99 c$ .

We have to find the potential difference.

Simplify

The mass of an electron is $m = 9.10 \times 10^{- 31}$ , the kinetic energy of an electron travelling at a constant velocity $v = 0.99 c$ is given by

role="math" localid="1649909533780" $E_{k} = m c^{2} [\frac{1}{\sqrt{1 - (v / c)^{2}}} - 1] = 9.1 \times 10^{- 31} \times {(3 \times 10^{8})}^{2} [\frac{1}{\sqrt{1 - (0.99)^{2}}} - 1] = 4.99 \times 10^{- 13} J$

Now, if there is a potential difference $v$ then we have

role="math" localid="1649909731842" $v q = E_{k} v = \frac{E_{k}}{q} = \frac{4.99 \times 10^{- 13}}{1.6 \times 10^{- 19}} = 3.12 \times 10^{6} v$

So the potential difference required is $3.12 \times 10^{6} V$ .

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.

Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of $0.99 c$ ?

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

Nuclear Physics

Linear Momentum

Solid State Physics

Rotational Dynamics

Fluids

Oscillations

Study anywhere. Anytime. Across all devices.

Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of 0.99c?

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

Nuclear Physics

Linear Momentum

Solid State Physics

Rotational Dynamics

Fluids

Oscillations

Study anywhere. Anytime. Across all devices.

Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of $0.99 c$ ?