The electron orbiting the proton in the hydrogen atom is at a distance of 5.3 × 10^-9 m. What is the ratio of the electric force to the gravitational force between these particles? (The mass of the proton is 1.67 × 10^-27 kg and the mass of the electron is 9.11 × 10^-31 kg.) A) 2.3 × 10³⁹ B) 2.5 × 10²⁹ C) 1.7 × 10¹⁹ D) 9.0 × 10¹⁶ E) 3.00 × 10⁸

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Quizplus · Accepted Answer

The ratio of the electric force to the gravitational force between an electron and a proton can be calculated using Coulomb's law for electric force and Newton's law of universal gravitation for gravitational force. The electric force (Fe) is given by Coulomb's law as $Fe = \frac{k \cdot e^2}{r^2}$, where $k$ is Coulomb's constant ($8.987 \times 10^9 Nm^2/C^2$), $e$ is the charge of an electron ($1.602 \times 10^{-19} C$), and $r$ is the distance between the particles. The gravitational force (Fg) is given by Newton's law of universal gravitation as $Fg = \frac{G \cdot m_e \cdot m_p}{r^2}$, where $G$ is the gravitational constant ($6.674 \times 10^{-11} N(m/kg)^2$), $m_e$ is the mass of the electron, and $m_p$ is the mass of the proton. The ratio $Fe/Fg$ simplifies to $\frac{k \cdot e^2}{G \cdot m_e \cdot m_p}$, which, when the values are substituted, yields a ratio significantly larger than 1, indicating the electric force is much stronger than the gravitational force between these particles. The correct calculation leads to a ratio in the order of $10^{39}$, matching choice A.

The Electron Orbiting the Proton in the Hydrogen Atom Is