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Question: The ratio of magnitude of electrostatic force and gravitational force an electron and a proton is....

The ratio of magnitude of electrostatic force and gravitational force an electron and a proton is.

A

6.6×10396.6 \times 10^{39}

B

2.3×10392.3 \times 10^{39}

C

6.6×10296.6 \times 10^{29}

D

2.3×10292.3 \times 10^{29}

Answer

2.3×10392.3 \times 10^{39}

Explanation

Solution

: Here, for an electron and a proton

Electrostatic force, ∣Fe∣=14πε0e2r2\left| F_{e} \right| = \frac{1}{4\pi\varepsilon_{0}}\frac{e^{2}}{r^{2}}

Gravitational force, ∣Fg∣=Gmempr2\left| F_{g} \right| = \frac{Gm_{e}m_{p}}{r^{2}}

∴∣Fe∣∣Fg∣=14πε0e2Gmemp\therefore\frac{\left| F_{e} \right|}{\left| F_{g} \right|} = \frac{1}{4\pi\varepsilon_{0}}\frac{e^{2}}{Gm_{e}m_{p}}

=9×109×(1.6×10−19)26.67×10−11×9×10−31×1.66×10−27= \frac{9 \times 10^{9} \times (1.6 \times 10^{- 19})^{2}}{6.67 \times 10^{- 11} \times 9 \times 10^{- 31} \times 1.66 \times 10^{- 27}}

=2.3×1039= 2.3 \times 10^{39}