Question

Two electrons in an atom are separated by 1.5 x 10‾¹º m, the typical size of an atom. What is the electric force between them?

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Electric force FF between charges qAq_A and qBq_B at a distance rr from each other is given as:

F=kqAqBr2\begin{equation} F = \dfrac{k q_A q_B}{r^2} \end{equation}

where k=9109 Nm2C2k = 9 \cdot 10^9 ~\mathrm{\dfrac{N m^2}{C^2}} is Coulomb constant.

We are told that the distance rr between the electrons is r=1.51010 mr = 1.5 \cdot 10^{-10} ~\mathrm{m} and we know that charge of an electron qeq_e is equal to negative value of the elementary charge qe=e=1.61019 Cq_e = - e = - 1.6 \cdot 10^{-19} ~\mathrm{C}. We can plug in this data into equation (1)(1), a general equation for force between the two charges and find that the force between these two electrons is equal to:

F=kqeqer2F=ke2r2F=9109 Nm2C2(1.61019)2 C2(1.51010)2 m2\begin{align*} F &= \dfrac{k q_e q_e }{r^2} \\ F &= \dfrac{k e^2 }{r^2} \\ F &= 9 \cdot 10^9 ~\mathrm{\dfrac{N m^2}{C^2}} \cdot \dfrac{ (1.6 \cdot 10^{-19})^2 ~\mathrm{C^2} }{(1.5 \cdot 10^{-10})^2 ~\mathrm{m^2} } \end{align*}

F=1.024108 N\boxed{F = 1.024 \cdot 10^{-8} ~\mathrm{N}}

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