How much work is done (by a battery, generator, or some other source of potentia

Question

How much work is done (by a battery, generator, or some other source of potential difference) in moving Avogadro's number of electrons from an initial point where the electric potential is 6.70 V to a point where the electric potential is -8.10 V? (The potential in each case is measured relative to a common reference point.) Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 150 V. Calculate the speed of an electron that is accelerated through the same potential difference. 1 m/s

Explanation / Answer

1) Workdone = q*delta_V

= N*e*(Vf-Vi)

= 6.023*10^23*(-1.6*10^-19)*(-8.1 - 6.7)

= 1.426*10^6 J

= 1.426 MJ

2) use Work-energy theorem,

Workdone = gain in kinetic energy

q*delta_V = 0.5*m*v^2

==> v = sqrt(2*q*delta_V/m)

= sqrt(2*1.6*10^-19*150/(1.67*10^-27))

= 1.69*10^5 m/s

3) use Work-energy theorem,

Workdone = gain in kinetic energy

q*delta_V = 0.5*m*v^2

==> v = sqrt(2*q*delta_V/m)

= sqrt(2*1.6*10^-19*150/(9.1*10^-31))

= 7.26*10^6 m/s

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