Question

What is the ratio of electrostatic force and gravitational force between a proton and electron at 1 mm distance?

Mass of proton – $1.67\times {10}^{-27}kg$

Mass of electron – $9.11\times {10}^{-31}kg$

Charge of electron – $1.6\times {10}^{-19}C$

• A. 10³⁸
• B. 10³⁹
• C. 10⁴⁰
• D. 10⁴¹

Answer 1

Answer: (B)

. 10³⁹

Given,

Mass of proton – $1.67\times {10}^{-27}kg$

Mass of electron – $9.11\times {10}^{-31}kg$

Charge of electron – $1.6\times {10}^{-19}C$

We know that,

Gravitational force =$F_g=G\frac{m_1{m}_2}{r^2}$ and

Electrostatic force = $F_e=k\frac{q_1{q}_2}{r^2}$

$\Rightarrow \frac{F_e}{F_g}=\frac{k{q}_1{q}_2}{G{m}_1{m}_2}$

$\Rightarrow \frac{F_e}{F_g}=\frac{9\times {10}^9\times 1.6\times {10}^{-19}\times 1.6\times {10}^{-19}}{6.67\times {10}^{-11}\times 1.67\times {10}^{-27}kg\times 9.11\times {10}^{-31}kg}$

$\Rightarrow \frac{F_e}{F_g}=2.3\times {10}^{39}$.