Chapter 7, Problem 71A

To determine

The gravitation attractive force between the proton and the electron of a hydrogen atom.

Answer to Problem 71A

  $2.96\times {10}^{-47}\text{N}$

Explanation of Solution

Given:

The mass of an electron is $9.1\times {10}^{-31}\text{}\text{kg}$ , mass of a proton is $1.7\times {10}^{-27}\text{}\text{kg}$ and the distance between them in a hydrogen atom is $0.59\times {10}^{-10}\text{}\text{m}$ .

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

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

Then using the given values of masses of proton and electron, and the distance between them, the gravitational force between them will be,

  $\begin{array}{c}F=\frac{G{m}_1{m}_2}{r^2}\\ =\frac{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\text{}\times 1.7\times {10}^{-27}}{{\left(0.59\times {10}^{-10}\right)}^2}\\ =2.96\times {10}^{-47}\text{N}\end{array}$

Conclusion:

Thus, the gravitational attractive force between proton and an electron in hydrogen atom is $2.96\times {10}^{-47}\text{N}$ .