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Chapter 36: Q. 57 (page 1061)

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

Short Answer

Expert verified

The potential difference required is3.12×106V.

Step by step solution

01

Given Information

We have given that, speedv=0.99c.

We have to find the potential difference.

02

Simplify

The mass of an electron is m=9.10×10-31, the kinetic energy of an electron travelling at a constant velocityv=0.99cis given by

role="math" localid="1649909533780" Ek=mc211-(v/c)2-1=9.1×10-31×3×108211-(0.99)2-1=4.99×10-13J

Now, if there is a potential difference vthen we have

role="math" localid="1649909731842" vq=Ekv=Ekq=4.99×10-131.6×10-19=3.12×106v

So the potential difference required is 3.12×106V.

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