Chapter 17, Problem 2P

To determine

The work done by the electric field in moving the proton, and express the answer in joules and electron volts.

Answer to Problem 2P

The work done in joules, and in electron volt is $2.88\times {10}^{-17}\text{J}$ , and $180\text{eV}$ , respectively.

Explanation of Solution

Given info:

The charge of proton is $q=1.6\times {10}^{-19}\text{C}$ .

Initial potential is $V_i=-55\text{V}$ .

The final potential is $V_f=125\text{V}$ .

Formula used:

Work done in moving the charge $q$ by the electric field is,

  $W=-q\left(V_f-V_i\right)$

Calculation:

Substituting the given values, we get

  $\begin{array}{c}W=-\left(1.6\times {10}^{-19}\right)\left(-55-125\right)\text{J}\\ =2.88\times {10}^{-17}\text{J}\end{array}$

Convert the joules into electron volt as follows.

  $\begin{array}{c}W=\left(2.88\times {10}^{-17}\text{J}\right)\left(\frac{1\text{eV}}{1.6021\times {10}^{-19}\text{J}}\right)\\ =179.7\text{eV}\\ \approx \text{180}\text{eV}\end{array}$

Conclusion:

Thus, the work done in joules is $2.88\times {10}^{-17}\text{J}$ and the work done in electron volt is $180\text{eV}$ .