Show the calculations and a clearly labelled diagram to determine what will happen to each of the droplets described in questions 5-7 (accel up, down or freeze mid-air). 5. A 1.88times 10^-16 g droplet has gained 45 electrons and is released in a 375N/C[D] electric field. 6. A 2.525times 10^-15 xg droplet has lost 216 electrons and is released in a 715.3N/C[U] electric field. 7. A 7.13times 10^-15 g droplet has lost 173 electrons and is released in an electric field that has a strength of 1686N/C [U].

Here's the breakdown for each droplet, including calculations and diagrams:<br /><br />**Understanding the Concepts**<br /><br />* **Forces at Play:** The droplet experiences two main forces: gravity (downwards) and the electric force (upwards or downwards depending on the field direction and charge).<br />* **Equilibrium:** If the forces are balanced, the droplet will "freeze" mid-air. If gravity is stronger, it will accelerate downwards. If the electric force is stronger, it will accelerate upwards.<br />* **Electric Force:** The electric force (F_E) on a charged object in an electric field is given by F_E = qE, where q is the charge and E is the electric field strength.<br />* **Gravitational Force:** The gravitational force (F_g) is given by F_g = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).<br />* **Electron Charge:** The elementary charge (e) is approximately 1.6 x 10^-19 C.<br /><br />**5. Droplet 1**<br /><br />* **Mass (m):** 1.88 x 10^-19 kg (converted from grams)<br />* **Charge (q):** 45 * -1.6 x 10^-19 C = -7.2 x 10^-18 C (negative since it gained electrons)<br />* **Electric Field (E):** 375 N/C [Down]<br />* **F_g:** (1.88 x 10^-19 kg) * (9.8 m/s²) = 1.84 x 10^-18 N [Down]<br />* **F_E:** (-7.2 x 10^-18 C) * (375 N/C) = -2.7 x 10^-15 N The negative sign indicates the force is upwards (opposite to the field direction since the charge is negative).<br /><br />**Diagram 1:**<br /><br />```<br /> ↑ F<sub>E</sub><br /> o (Droplet)<br /> ↓ F<sub>g</sub><br /> E ↓<br />```<br /><br />**Result:** Since F_E > F_g, the droplet will accelerate **upwards**.<br /><br /><br />**6. Droplet 2**<br /><br />* **Mass (m):** 2.525 x 10^-18 kg<br />* **Charge (q):** 216 * 1.6 x 10^-19 C = 3.456 x 10^-17 C (positive since it lost electrons)<br />* **Electric Field (E):** 715.3 N/C [Up]<br />* **F_g:** (2.525 x 10^-18 kg) * (9.8 m/s²) = 2.47 x 10^-17 N [Down]<br />* **F_E:** (3.456 x 10^-17 C) * (715.3 N/C) = 2.47 x 10^-14 N [Up] (Force is in the same direction as the field since the charge is positive)<br /><br />**Diagram 2:**<br /><br />```<br /> ↑ E<br /> ↑ F<sub>E</sub><br /> o (Droplet)<br /> ↓ F<sub>g</sub><br /><br />```<br /><br />**Result:** Since F_E > F_g, the droplet will accelerate **upwards**.<br /><br /><br />**7. Droplet 3**<br /><br />* **Mass (m):** 7.13 x 10^-18 kg<br />* **Charge (q):** 173 * 1.6 x 10^-19 C = 2.768 x 10^-17 C (positive since it lost electrons)<br />* **Electric Field (E):** 1686 N/C [Up]<br />* **F_g:** (7.13 x 10^-18 kg) * (9.8 m/s²) = 7.0 x 10^-17 N [Down]<br />* **F_E:** (2.768 x 10^-17 C) * (1686 N/C) = 4.67 x 10^-14 N [Up]<br /><br />**Diagram 3:**<br /><br />```<br /> ↑ E<br /> ↑ F<sub>E</sub><br /> o (Droplet)<br /> ↓ F<sub>g</sub><br />```<br /><br />**Result:** Since F_E > F_g, the droplet will accelerate **upwards**.<br />