Chapter 7, Problem 37A

To determine

The mass of an electron if the gravitational force between two electrons is given.

Answer to Problem 37A

  $9.11\times {10}^{-31}\text{kg}$

Explanation of Solution

Given:

The electrons are 1.0 m apart and the gravitational force between them is $5.54\times {10}^{-71}\text{N}$ .

Formula used:

Gravitational force:

  $F=\frac{G{m}_1{m}_2}{r^2}$

Where, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between the masses.

Calculation:

The value of gravitational constant is,

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Let the mass of the electrons be “ m ”. Then using the given values of the gravitational force and the distance between the electrons, the mass of the electrons will be,

  $\begin{array}{c}F=\frac{Gmm}{r^2}\\ 5.54\times {10}^{-71}=\frac{6.67\times {10}^{-11}\times m^2}{{\left(1\right)}^2}\\ m=\sqrt{0.83\times {10}^{-60}}\\ m=9.11\times {10}^{-31}\text{kg}\end{array}$

Conclusion:

Thus, the mass of the electron is $9.11\times {10}^{-31}\text{kg}$ .