The electron and proton of an atom are separated by $8.5 imes 10^{-10} \mathrm{~m}$ . Find the ratio between the electric force and the gravitational force between the two particles. [Electron charge $=-1.6 imes$ $10^{-19} \mathrm{C}$, Electron mass $=9.11 imes 10^{-31} \mathrm{~kg}$, Proton mass $=1.67 imes 10^{-27} \mathrm{~kg}$, Gravitational Constant $\mathrm{G}=6.67 imes 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$ ]

Question

The electron and proton of an atom are separated by $8.5 	imes 10^{-10} \mathrm{~m}$ . Find the ratio between the electric force and the gravitational force between the two particles. [Electron charge $=-1.6 	imes$ $10^{-19} \mathrm{C}$, Electron mass $=9.11 	imes 10^{-31} \mathrm{~kg}$, Proton mass $=1.67 	imes 10^{-27} \mathrm{~kg}$, Gravitational Constant $\mathrm{G}=6.67 	imes 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$ ]

Accepted Answer

গ. $2.27 	imes 10^{39}$

ব্যাখ্যা: তড়িৎ বল, $F_e = \frac{1}{4\pi\varepsilon_0} \frac{e^2}{r^2}$ এবং মহাকর্ষ বল, $F_g = \frac{G m_e m_p}{r^2}$।
উভয় বলের অনুপাত, $\frac{F_e}{F_g} = \frac{k e^2}{G m_e m_p}$ (দূরত্ব $r$ এর ওপর নির্ভর করে না)।
মান বসিয়ে পাই,
$\frac{F_e}{F_g} = \frac{8.99 	imes 10^9 	imes (1.6 	imes 10^{-19})^2}{6.67 	imes 10^{-11} 	imes 9.11 	imes 10^{-31} 	imes 1.67 	imes 10^{-27}} \approx 2.27 	imes 10^{39}$।

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