एक इलेक्ट्रॉन एवं एक प्रोटॉन के लिए स्थिरवैद्युत बल एवं गुरुत्वाकर्षण बल के परिमाण का अनुपात क्या है?

The ratio is

$$\frac{F_e}{F_g} = \frac{k q_e^2}{G m_e m_p}$$

where $k = 9 \times 10^9 \, \mathrm{N \cdot m^2 / C^2}$, $q_e = 1.6 \times 10^{-19} \, \mathrm{C}$, $G = 6.7 \times 10^{-11} \, \mathrm{N \cdot m^2 / kg^2}$, $m_e = 9.1 \times 10^{-31} \, \mathrm{kg}$, $m_p = 1.67 \times 10^{-27} \, \mathrm{kg}$.

$$q_e^2 = (1.6 \times 10^{-19})^2 = 2.56 \times 10^{-38} \, \mathrm{C^2}.$$

Numerator: $k q_e^2 = 9 \times 10^9 \times 2.56 \times 10^{-38} = 23.04 \times 10^{-29} = 2.304 \times 10^{-28} \, \mathrm{N \cdot m^2}$.

$$m_e m_p = 9.1 \times 10^{-31} \times 1.67 \times 10^{-27} = 15.197 \times 10^{-58} = 1.52 \times 10^{-57} \, \mathrm{kg^2}.$$

Denominator: $G m_e m_p = 6.7 \times 10^{-11} \times 1.52 \times 10^{-57} = 10.184 \times 10^{-68} = 1.02 \times 10^{-67} \, \mathrm{N \cdot m^2}$.

$$\frac{F_e}{F_g} = \frac{2.304 \times 10^{-28}}{1.02 \times 10^{-67}} = \frac{2.304}{1.02} \times 10^{-28 - (-67)} = 2.26 \times 10^{39} \approx 2.3 \times 10^{39}.$$

(b) $2.3 \times 10^{39}$

(b)