Question

Compute the charge of two argon nuclei, if the force of repulsion is 85nN and separated by 2nm.

Answer 1

Answer:

q = 6.14 x 10-18

Explanation:

The electrostatic force between two charged particles can be calculated on the principle of Columb's Law which can be written in mathematical form as;

F = K q1 x q 2 / d^2

Now we are given that

F = 85 × 10-9 N

d = 2 × 10-9 m

Now using the formula we get,

85 × 10-9  = (9 × 109) x (q)2 / (2 x 10-9)2

340 × 10-27 = (9 × 109) x (q)2

37.7 × 10-36 =  (q)2

q = 6.14 x 10-18

Answer 2

Given:

The force between two argon nuclei, F = 85 nN = 85 × 10⁻⁹ N

The distance between two argon nuclei, r = 2 nm = 2 × 10⁻⁹ m

To Find:

The charge of the two argon nuclei.

Calculation:

- According to Coulomb's law, force between two charges is given as:

F = k q1q2/r²

⇒ F = k q²/r²

⇒ q² = Fr²/k

⇒ q² = 85 × 10⁻⁹ × (2 × 10⁻⁹)² / 9 × 10⁹

⇒ q² = 85 × 10⁻⁹ × 4 × 10⁻¹⁸ / 9 × 10⁹

⇒ q² = 340 × 10⁻³⁶ / 9

⇒ q² = 37.78 × 10⁻³⁶

⇒ q = √(37.78 × 10⁻³⁶)

⇒ q = 6.146 × 10⁻¹⁸ C

- So, the charge of each argon nuclei is 6.146 × 10⁻¹⁸ Coulomb.