Using Coulomb’s Law (College Board AP® Chemistry): Revision Note

Always verify the units before any calculation. If the units are not consistent, make sure to perform any transformation before replacing the values into the Coulomb's Law formula

Calculating the force that exists between a proton and an electron given the following information.

Charge of a proton = +1.602 x 10^-19 C
Charge of an electron = -1.602 x 10^-19 C
Distance between them = 1 x 10^-10 m

Answer:

• Step 1: Write down the values and the Coulomb's law formula

q₁ = +1.602 x 10^-19 C

q₂ = -1.602 x 10^-19 C

r = 1 x 10^-10 m

k = 8.99 x 10⁹ N·m² C^-²

 ${\mathrm{F}}_{\mathrm{coulombic}}=\mathrm{k}\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{r}}^2}$

• Step 2: Replace the value in the Coulomb’s Law

 ${\mathrm{F}}_{\mathrm{coulombic}}=\mathrm{k}\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{r}}^2}$

${\mathrm{F}}_{\mathrm{coulombic}}=8.99\times {10}^9\mathrm{N}\mathrm{m}²{\mathrm{C}}^{-2}\frac{(+1.602\times {10}^{-19}\mathrm{C})(-1.602\times {10}^{-19}\mathrm{C})}{{(1\times {10}^{-10}\mathrm{m})}^2}$

• Step 3: Calculate the force.

F_coulombic = -2.31 x 10^-8 N

• The negative sign indicates an attractive force since proton and electron have opposite charges

If the problem does not state the charge of the electron, you can find it in the AP Chemistry Equations and Constants that appear at the beginning of your examination. The charge of the proton has the same value but with a positive sign