A particle accelerator uses a capacitor to accelerate charged particles. The cap

Question

A particle accelerator uses a capacitor to accelerate charged particles. The capacitor has a potential difference of 435 V between its two plates. A proton is initially held at rest against the positive terminal of the capacitor and then released. What is the kinetic energy of the proton when it reaches the negative terminal? Note: mp = mn = 1.67 times 10-27kg What is the speed of the proton when it reaches the negative terminal? Instead, a Helium nucleus, made of two protons and two neutrons, is accelerated. What is the speed of the Helium nucleus when it reaches the negative terminal?

Explanation / Answer

a)
workdone on proton, W = q* delta V

W = 1.6*10^-19*435

W = 6.96*10^-17 J

we know, Work done = KE = 6.96*10^-17 J


b)

KE = 0.5*m*v^2

==> v = sqrt(2*KE/m)

= sqrt(2*6.96*10^-17/1.67*10^-27)

= 2.89*10^5 m/s

c) workdone will be doubled
mass becomes 4 times

so, velsoity becomes v*sqrt(2/4)

v' = v/sqrt(2)

= 2.89*10^5/1.414

= 2.04*10^5 m/s

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