How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of $1.00 \mathrm {~V}$ ? The proton is 1836 times heavier than an electron, and $e = 1.60 \times10^{-19}$ C.

Question

How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of

1.00 \mathrm {~V}

? The proton is 1836 times heavier than an electron, and

e = 1.60 \times10^{-19}

C.

Quizplus · Accepted Answer

The kinetic energy gained by a charged particle when it is accelerated through a potential difference of $V$ volts is given by $KE = qV$, where $q$ is the charge of the particle and $V$ is the potential difference in volts. Since the charge of a proton is $1.60 \times 10^{-19}$ C (the same as the magnitude of the charge of an electron), and it is accelerated through a potential difference of $1.00 \mathrm{V}$, the kinetic energy gained is $1.60 \times 10^{-19} \mathrm{C} \times 1.00 \mathrm{V} = 1.60 \times 10^{-19} \mathrm{J}$, which is equivalent to $1.00 \mathrm{eV}$ because $1 \mathrm{eV}$ is defined as the energy gained by a charge of $1 \mathrm{e}$ (where $e = 1.60 \times 10^{-19}$ C) when it is accelerated through a potential difference of $1 \mathrm{V}$. The mass of the proton or how many times it is heavier than an electron is irrelevant to the calculation of energy gained in electron volts (eV) when accelerated through a given potential difference.

How Much Kinetic Energy Does a Proton Gain If It 1.00 V1.00 \mathrm {~V}1.00 V

How Much Kinetic Energy Does a Proton Gain If It $1.00 \mathrm {~V}$