How much work is needed to move a proton from a point with a potential of +470 V to a point where it is -51.0 V?
Express your answer in joules.
Express your answer in electron volts.
To calculate the work needed to move a proton from one point to another with different potentials, you need to use the equation:
Work (Joules) = Charge (Coulombs) x Potential Difference (Volts)
1. Convert the potential difference from volts to joules. To do this, multiply the potential difference by the charge of an electron (1.602 x 10^-19 C).
Potential Difference (Joules) = Potential Difference (Volts) x Charge of Electron (Coulombs)
In this case, the potential difference is +470 V, so the potential difference in joules is:
Potential Difference (Joules) = +470 V x 1.602 x 10^-19 C
2. Calculate the work in joules. Since the proton has a positive charge, the direction of movement is from the +470 V point to the -51.0 V point.
Work (Joules) = Charge of Proton (Coulombs) x Potential Difference (Joules)
The charge of a proton is the same as the charge of an electron but with a positive sign: +1.602 x 10^-19 C
Work (Joules) = +1.602 x 10^-19 C x Potential Difference (Joules)
3. Convert the work in joules to electron volts (eV). One electron volt is equal to 1.602 x 10^-19 joules.
Work (eV) = Work (Joules) / 1.602 x 10^-19 Joules
Now, let's do the calculations:
Potential Difference (Joules) = +470 V x 1.602 x 10^-19 C
Work (Joules) = +1.602 x 10^-19 C x Potential Difference (Joules)
Work (eV) = Work (Joules) / 1.602 x 10^-19 Joules
Plug in the values to get the final answer in joules and electron volts.