1. Energy Conservation
* The potential energy lost by the electron as it moves through the potential difference is converted into kinetic energy.
* Potential energy (PE) = Charge (q) * Potential difference (V)
* Kinetic energy (KE) = 1/2 * mass (m) * velocity squared (v²)
2. Setting up the Equation
* PE = KE
* q * V = 1/2 * m * v²
3. Plugging in Values
* Charge of an electron (q) = 1.602 x 10⁻¹⁹ Coulombs
* Potential difference (V) = 1 Volt
* Mass of an electron (m) = 9.109 x 10⁻³¹ kg
4. Solving for Velocity (v)
* 1.602 x 10⁻¹⁹ C * 1 V = 1/2 * 9.109 x 10⁻³¹ kg * v²
* 1.602 x 10⁻¹⁹ J = 4.5545 x 10⁻³¹ kg * v²
* v² = (1.602 x 10⁻¹⁹ J) / (4.5545 x 10⁻³¹ kg)
* v² ≈ 3.52 x 10¹¹ m²/s²
* v ≈ 5.93 x 10⁵ m/s
Therefore, an electron accelerated from rest through a 1 V potential difference will acquire a speed of approximately 5.93 x 10⁵ m/s.
