The electron and proton of an atom are separated by 8.5×10−10 m 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× =-1.6 imes 10−19C 10^{-19} \mathrm{C} , Electron mass =9.11×10−31 kg =9.11 imes 10^{-31} \mathrm{~kg} , Proton mass =1.67×10−27 kg =1.67 imes 10^{-27} \mathrm{~kg} , Gravitational Constant G=6.67×10−11Nm2 kg−2 \mathrm{G}=6.67 imes 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2} ]

Question

The electron and proton of an atom are separated by 8.5×10−10 m 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× =-1.6 	imes 10−19C 10^{-19} \mathrm{C} , Electron mass =9.11×10−31 kg =9.11 	imes 10^{-31} \mathrm{~kg} , Proton mass =1.67×10−27 kg =1.67 	imes 10^{-27} \mathrm{~kg} , Gravitational Constant G=6.67×10−11Nm2 kg−2 \mathrm{G}=6.67 	imes 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2} ]

Accepted Answer

গ. 2.27×1039 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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