Question

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of: 

(1) 10³⁹ 

(2) 10¹⁹ 

(3) 10²⁹ 

(4) 10³⁶ 

Answer 1

Correct option is :  (1) \(10^{39}\)    

\(\mathrm{F}_{\mathrm{e}}=\frac{\mathrm{kQ}_{1} \mathrm{Q}_{2}}{\mathrm{r}^{2}}=\frac{9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.6 \times 10^{-19}}{\mathrm{r}^{2}}\)

\(\mathrm{F}_{\mathrm{g}}=\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2}}{\mathrm{r}^{2}}=\frac{6.67 \times 10^{-11} \times 9.1 \times 10^{-31} \times 1.6 \times 10^{-27}}{\mathrm{r}^{2}}\)

\(\frac{\mathrm{F}_{\mathrm{e}}}{\mathrm{F}_{\mathrm{g}}} \cong 0.23 \times 10^{40} \cong 2.3 \times 10^{39}\)