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Modern Physics
Found in: Page 67
Modern Physics

Modern Physics

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.

See the step by step solution

Step by Step Solution

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.

KE=ΔUKE=qΔV(γ1)mec2=eΔV ...........(1)

Step 2: Determine the potential difference applied


  • Lorentz factor γ = 11 - u2c2=11 - 0.9998c2c2= 50
  • Mass of electron me=9.1×1031kg
  • Charge of electron e=1.6×1019C

Putting these values in above equation we get,

localid="1659084824833" (501)×9.1×1031kg×(3×108ms)2=(1.6×1019)×ΔVΔV=25.08MV

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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