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Chapter 2: Q85E (page 67)

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

Short Answer

Expert verified

The potential energy required to acquire a speed of 0.9998c is25 Mega Volts.

Step by step solution

01

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(γ − 1)mec2 = eΔV ...........(1)

02

Determine the potential difference applied

Here,

  • Lorentz factor


    γ=11-u2c2=11-0.9998c2c2=50
  • Mass of electron me = 9.1 × 10−31 kg
  • Charge of electron e = 1.6 × 10−19 C

Putting these values in above equation we get,

localid="1659084824833" (50 − 1) × 9.1 × 10−31 kg × (3 × 108 ms)2 = (1.6 × 10−19) × ΔVΔV = 25.08 MV

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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