An electron is to be accelerated from a velocity of 5.00×106 m/s to a velocity of 9.90×106 m/s . through what potential difference must the electron pass to accomplish this

Potential difference needed= 207.9 V

Explanation=

using work energy principle

Work done on the electron= change in kinetic energy

W= 1/2m Vf²- 1/2 mVi²

m= mass of electron=9.11 x 10⁻³¹ Kg

Vf= final velocity= 9.9 x 10⁶ m/s

Vi= initial velocity= 5 x 10⁶ m/s

so W = 1/2 (9.11 x 10⁻³¹ ) (9.9 x 10⁶ )²- 1/2 (9.11 x 10⁻³¹ ) (5 x 10⁶ )²

W=3.33 x 10⁻¹⁷ J

Now work done= q V

q= charge of electron= 1.6 x 10⁻¹⁹J

V= potential difference

3.33 x 10⁻¹⁷= (1.6 x 10⁻¹⁹) V

v= 207.9 V

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