What is the force acting between two α-particles if the distance between them is 3.2 × 10^-15 m?

CONCEPT:

• Coulomb’s law: When two charged particles of charges q1 and q2 are separated by a distance r from each other then the electrostatic force between them is directly proportional to the multiplication of charges of two particles and inversely proportional to the square of the distance between them.
  
  Force (F) ∝ q1 × q₂
  \(F \propto \frac{1}{{{r^2}}}\)
  \(F = K\frac{{{q_1} × {q_2}}}{{{r^2}}}\)
  Where K is a constant = 9 × 109 Nm2/C2

CALCULATION:

Given that:

Two α-particles are there, so both charges are equal: q1 = q2 = q

Charge on one alpha particles = q = + (2 × charge on an electron) = +2e 

q = q₁ = q₂ = 2 × 1.6 × 10^-19 C

Distance between them (r) = 3.2 × 10-15 m

\(F = K\frac{{{q^2}}}{{{r^{2\;}}}} = \frac{9\times 10^9 \times (2 \times 1.6 \times 10^{-19})^2}{(3.2\times 10^{-15})^2}\)

F = 90 N

• The Force between two alpha particles will be equal to 90 N.
• Hence option 4 is correct.