An alpha particle is a nucleus of doubly ionized helium. It has mass of $6.68 * 10^{-27}$kg and charge of $3.2 * 10^{-19}C$. Compare the force of electrostatic repulsion between the two alpha particles with the force of gravitational attraction between them.

Given,

Mass of the alpha particle = $6.68\;*\;10^{-27}\;kg$

Charge of the alpha particle = $3.2 * 10^{-19}\;C$

We have,

Electrostatic Force $(E_f) = $$\frac{1}{4\pi \epsilon_0} \frac{q_1\;q_2}{R^2}$

Electrostatic Force $(E_f) = 9*10^9 * $$\frac{q^2}{R^2}$ = $9*10^9 * $$\frac{(3.2 * 10^{-19})^2}{R^2}$ ......... (i)

Gravitational force $(G_f) = G $$\frac{M_1\;M_2}{R^2}$

Gravitational force $(G_f) = 6.67\;*\;10^{-11} $$\frac{(6.68*10^{-27})^2}{R^2}$ .......... (ii)

Dividing equation (i) and (ii), we get

$\frac{E_f}{G_f} = \frac{9.216 \;*\; 10^{-28}}{2.976 \;*\; 10^{-63}}$

$= 3.096 \;*\; 10^{35}$

⇒ $E_f = 3.096 \;*\; 10^{35}\; G_f$

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