Question

Two protons are 1.28 fm apart. (1 fm= 1 femtometer = 1 x 10-15 m.) What is the ratio of the electric force to the gravitational force on one proton due to the other proton?

Answer 1

Given

Distance between two protons, r=1.28 fm

Mass of a proton,

$m=1.67\times10^{-27}kg$

Charge of an electron,

$q=1.6\times10^{-19}C$

To find

What is the ratio of the electric force to the gravitational force on one proton due to the other proton?

Explanation

The electric force is

$F=k\frac{q\times q}{r^2}$

The gravitational fore

$F^{\prime}=G\frac{m\times m}{r^2}$

The ratio is

$\begin{gathered} \frac{F}{F^{\prime}}=\frac{kq\times q}{Gm\times m} \\ \Rightarrow\frac{F}{F^{\prime}}=\frac{9\times10^9\times1.6\times10^{-19}\times1.6\times10^{-19}}{6.67\times10^{-11}\times1.67\times10^{-27}\times1.67\times10^{-27}} \\ \Rightarrow\frac{F}{F^{\prime}}=1.2\times10^{36} \end{gathered}$

Conclusion

The required ratio is

$1.2\times10^{36}$