Answer:
The ratio of gravitational force to electrical force is 3.19 x 10^-36
Explanation:
mass of an alpha particle = 6.64 x [tex]10^{-27}[/tex] kg
charge on an alpha particle = +2e = +2(1.6 x [tex]10^{-19}[/tex] C) = 3.2 x [tex]10^{-19}[/tex] C
distance between particles = d
For gravitational attraction:
The force of gravitational attraction F = [tex]\frac{Gm^{2} }{r^{2} }[/tex]
where G = gravitational constant = 6.67 x [tex]10^{-11}[/tex] m^3 kg^-1 s^-2
r = the distance between the particles = d
m = the mass of each particle
therefore, gravitational force = [tex]\frac{6.67*10^{-11}*(6.64*10^{-27} )^{2} }{d^{2} }[/tex] = [tex]\frac{2.94*10^{-63} }{d^{2} }[/tex] Newton
For electrical repulsion:
Electrical force between the particles = [tex]\frac{-kQ^{2} }{r^{2} }[/tex]
where k is the Coulomb's constant = 9.0 x [tex]10^{9}[/tex] N•m^2/C^2
r = distance between the particles = d
Q = charge on each particle
therefore, electrical force = [tex]\frac{-9*10^{9}*(3.2*10^{-19} )^{2} }{d^{2} }[/tex] = [tex]\frac{-9.216*10^{-28} }{d^{2} }[/tex] Newton
the negative sign implies that there is a repulsion on the particles due to their like charges.
Ratio of the magnitude of gravitation to electrical force = [tex]\frac{2.94*10^{-63} }{9.216*10^{-28} }[/tex]
==> 3.19 x 10^-36
