the electrostatic forces are [tex]10^{36}[/tex] larger than the gravitational force
Explanation:
Let's do the calculation by using two molecules of hydrogen, each containing 2 atoms of hydrogen.
The gravitational force between the two molecules is given by:
[tex]F=\frac{G m_1 m_2}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
m1 and m2 are the masses of the two molecules: since they are identical,
[tex]m_1 = m_2 = 2m_p = 1.67\cdot 10^{-27} kg[/tex], twice the mass of the proton
r is the distance between the two molecules
The force can be rewritten as
[tex]F_G=\frac{Gm_p^2}{r^2}[/tex]
We can assume instead that electrostatic force between the two molecules is given by the interaction between the positively charged nuclei and the neatively charged electrons. Therefore,
[tex]F_E=\frac{kq_1 q_2}{r^2}[/tex]
where
[tex]k=8.99\cdot 10^9 Nm^{-2}C^{-2}[/tex] is the Coulomb's constant
[tex]q_1 = q_2 = 2e[/tex] is the magnitude of the charge of each molecule, where
[tex]e=1.6\cdot 10^{-19}C[/tex] is the fundamental charge
r is the distance between the two molecules
So the force can be rewritten as
[tex]F_E=\frac{ke^2}{r^2}[/tex]
Therefore, the ratio between the two forces is:
[tex]\frac{F_E}{F_G}=\frac{ke^2}{Gm_p^2}=\frac{(8.99\cdot 10^9)(1.6\cdot 10^{-19})^2}{(6.67\cdot 10^{-11})(1.67\cdot 10^{-27})^2}\sim 10^{36}[/tex]
So, the electrostatic forces are [tex]10^{36}[/tex] larger than the gravitational force.
Learn more about electric force:
brainly.com/question/8960054
brainly.com/question/4273177
Learn more about gravitational force:
brainly.com/question/1724648
brainly.com/question/12785992
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