Question 375: Electrostats & Capacitance

Question

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

Accepted Answer

To find the ratio of the Coulombic force to the gravitational force between an electron and a proton in a hydrogen-like system, we use the formulae for both forces and then divide them.
The Coulombic (electrostatic) force, $F_C$, between two charges is given by Coulomb's law:
$F_C = k \frac{|q_1 q_2|}{r^2}$
where $k$ is Coulomb's constant ($8.987 	imes 10^9 \, 	ext{Nm}^2	ext{C}^{-2}$), $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between the charges. For a proton and an electron, $q_1 = q_2 = e$, where $e$ is the elementary charge ($1.602 	imes 10^{-19} \, 	ext{C}$).
The gravitational force, $F_G$, between two masses is given by Newton's law of universal gravitation:
$F_G = G \frac{m_1 m_2}{r^2}$
where $G$ is the gravitational constant ($6.674 	imes 10^{-11} \, 	ext{Nm}^2	ext{kg}^{-2}$), and $m_1$ and $m_2$ are the masses of the two objects. For a proton and an electron, $m_p \approx 1.673 	imes 10^{-27} \, 	ext{kg}$ and $m_e \approx 9.109 	imes 10^{-31} \, 	ext{kg}$, respectively.
The ratio of the Coulombic to the gravitational force is therefore:
$\frac{F_C}{F_G} = \frac{k \frac{|e^2|}{r^2}}{G \frac{m_p m_e}{r^2}} = \frac{k e^2}{G m_p m_e}$
Plugging in the values:
$\frac{F_C}{F_G} = \frac{(8.987 	imes 10^9) (1.602 	imes 10^{-19})^2}{(6.674 	imes 10^{-11}) (1.673 	imes 10^{-27}) (9.109 	imes 10^{-31})}$
$\frac{F_C}{F_G} = \frac{(8.987 	imes 10^9) 	imes (2.568 	imes 10^{-38})}{(6.674 	imes 10^{-11}) 	imes (1.523 	imes 10^{-57})}$
$\frac{F_C}{F_G} \approx 2.3 	imes 10^{39}$
Therefore, the ratio of the Coulombic force to the gravitational force between an electron and a proton in a hydrogen-like system is on the order of $10^{39}$, making Option B the correct answer.

Answer

1019

Answer

1039

Answer

1029

Answer

1036

Electrostats & Capacitance

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

Choose the correct answer: