Question

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

Answer 1

mass of alpha particle, m = 6.68 × 10^-27 kg

charge on alpha particle, q = 3.2 × 10^-19c

Let r is the separation between two alpha particles.

so, electrostatic force between them , Fe = kq²/r²

= 9 × 10^9 × (3.2 × 10^-19)²/r²

= 9 × 10.24 × 10^-38 × 10^9/r²

= 92.16 × 10^-29/r²

= 9.216 × 10^-28/r² ......(1)

and gravitational force between them, Fg = Gm²/r²

= 6.67 × 10^-11 × (6.68 × 10^-27)²/r²

= 6.67 × 6.68 × 6.68 × 10^-11 × 10^-54/r²

= 297.63 × 10^-65/r²

= 2.9763 × 10^-63/r² .....(2)

from equations (1) and (2),

Fe/Fg = (9.216 × 10^-28)/(2.9763 × 10^-63)

= (9.216/2.9763) × 10^(63 - 28)

≈ 3 × 10^35