Question

An alpha particle (charge 2e) is sent at high speed toward an atomic nucleus. The electric force acting on the alpha particle is 79.8 N when it is 2.29 x 10(-14) m away from the nucleus. What is the charge on the atomic nucleus? (e = 1.60 x 10(-19) C, Kc = 9 x 10(9) N•m(2)/c(2)

Answer 1

1.45×10⁻¹⁶ C

Step-by-step explanation:

Applying,

F = kqq'/r²................ Equation 1

Where F = force acting on the alpha particle, k = coulomb's constant, q = charge on the alpha particle, q' = charge on the atomic nucleus, r = distance of seperation between the alpha particle and the atomic nucleus.

make q' the subject of the equation

q' = Fr²/(kq)................. Equation 2

From the question,

Given: F = 79.8 N, r = 2.29×10⁻¹⁴ m, q = 2e = (2×1.6×10⁻¹⁹) = 3.2×10⁻¹⁹ C, k = 9×10⁹ Nm²/C²

Substitute these values into equation 2

q' = [79.8×(2.29×10⁻¹⁴)²]/(3.2×10⁻¹⁹×9×10⁹)

q' = (4.18×10⁻²⁶)/(2.88×10⁻¹⁰)

q' = 1.45×10⁻¹⁶ C