Question

"Two electrons in an atom are separated by 1.4 × 10−10 m, the typical size of an atom. What is the force between them? The Coulomb constant is 9 × 109 N · m2 /C 2 . Answer in units of N."

Answer 1

Answer:

$F\approx 1.17551\times 10^{-8} N$

Explanation:

In order to find the force between the two electrons, we need to use Coulomb's law. In its scalar form, the law is given by:

$F=k_c \frac{q_1*q_2}{r^2}$

Where:

$k_c=Coulomb\hspace{3}constant\approx 9\times10^{9} \frac{Nm^2}{C^2} \\q_1\hspace{3}and\hspace{3}q_2=Magnitudes\hspace{3}of\hspace{3}the\hspace{3}charges\\r=Distance\hspace{3}between\hspace{3}the\hspace{3}charges$

The electric charge of an electron is a known constant given by:

$q_e \approx -1.6 \times 10^{-19} C$

So:

$q_1=q_2=q_e \approx -1.6 \times 10^{-19} C$

Therefore, replacing the data provided in the Coulomb's law equation:

$F=(9\times 10^{9})\frac{(-1.6\times 10^{-19})*(-1.6\times 10^{-19})}{(1.4\times 10^{-10})^2} =1.175510204\times10^{-8} \approx 1.17551\times10^{-8}N$