Book edition 2nd Edition

Author(s) Randy Harris

Pages 633 pages

ISBN 9780805303087

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Short Answer

An electron accelerated from rest through a potential difference V acquires a speed of 0.9998c. Find the value of V.

The potential energy required to acquire a speed of 0.9998c is 25 Mega Volts.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define relation between kinetic energy and potential difference

The relativistic kinetic energy of a charged particle is equal magnitude to the change in potential energy as it is accelerated through a potential difference.

$\begin{matrix} K E = Δ U \\ K E = q Δ V \\ (γ - 1) m_{e} c^{2} = e Δ V \end{matrix}$ ...........(1)

Step 2: Determine the potential difference applied

Here,

Lorentz factor $\begin{array}{rcl} γ & = & \frac{1}{\sqrt{1 - \frac{u^{2}}{c^{2}}}} \\ = & \frac{1}{\sqrt{1 - \frac{{(0.9998 c)}^{2}}{c^{2}}}} \\ = & 50 \end{array}$
Mass of electron $m_{e} = 9.1 \times 10^{- 31} k g$
Charge of electron $e = 1.6 \times 10^{- 19} C$

Putting these values in above equation we get,

localid="1659084824833" $\begin{matrix} (50 - 1) \times 9.1 \times 10^{- 31} k g \times {(3 \times 10^{8} \frac{m}{s})}^{2} = (1.6 \times 10^{- 19}) \times Δ V \\ Δ V = 25.08 M V \end{matrix}$

So, to get an electron accelerated to a speed of 0.9998c, the required potential difference to be applied is 25 mega volts.

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Modern Physics

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Short Answer

An electron accelerated from rest through a potential difference V acquires a speed of 0.9998c. Find the value of V.

Step by Step Solution

Step 1: Define relation between kinetic energy and potential difference

Step 2: Determine the potential difference applied

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Modern Physics

Answers without the blur.

Short Answer

An electron accelerated from rest through a potential difference V acquires a speed of 0.9998c. Find the value of V.

Step by Step Solution

Step 1: Define relation between kinetic energy and potential difference

Step 2: Determine the potential difference applied

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