4. A nitrogen ion with a mass of 2.4times 10^-26 kg has a -2e charge and is situated I in an atmospheric electric field of 200.0N/C. Calculate the magnitude of the initial acceleration of the ion. (7.4)Th A

Here's how to calculate the initial acceleration of the nitrogen ion:<br /><br />**1. Identify the Given Information:**<br /><br />* **Mass (m):** $2.4 \times 10^{-26}$ kg<br />* **Charge (q):** -2e (where e is the elementary charge, $1.6 \times 10^{-19}$ C)<br />* **Electric Field (E):** 200.0 N/C<br /><br />**2. Calculate the Force on the Ion:**<br /><br />The force on a charged particle in an electric field is given by Coulomb's Law:<br /><br />F = qE<br /><br />First, calculate the total charge (q):<br /><br />q = -2 * (1.6 x 10⁻¹⁹ C) = -3.2 x 10⁻¹⁹ C<br /><br />Now, calculate the force (F):<br /><br />F = (-3.2 x 10⁻¹⁹ C) * (200.0 N/C) = -6.4 x 10⁻¹⁷ N<br /><br />The negative sign indicates the force is opposite the direction of the electric field, which is expected for a negative charge. The magnitude of the force is what we need for the next step.<br /><br />**3. Calculate the Acceleration:**<br /><br />Newton's second law of motion states:<br /><br />F = ma<br /><br />where:<br /><br />* F is the force<br />* m is the mass<br />* a is the acceleration<br /><br />We can rearrange this equation to solve for acceleration (a):<br /><br />a = F/m<br /><br />Now, plug in the values:<br /><br />a = (6.4 x 10⁻¹⁷ N) / (2.4 x 10⁻²⁶ kg) = 2.67 x 10⁹ m/s²<br /><br />**4. Final Answer:**<br /><br />The magnitude of the initial acceleration of the nitrogen ion is $\boxed{2.7 \times 10^9 \, m/s^2}$ (rounded to two significant figures).<br />