Notes on Electronvolt and Potential Energy

Definition: An electronvolt is a unit of energy equal to the amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt.
Formula: The energy (E) in electronvolts can be calculated using the equation:
E = q * V
Where:
- E is the energy in electronvolts (eV)
- q is the charge of the electron (approximately -1.6 x 10^-19 coulombs)
- V is the potential difference in volts

Concept: A potential difference of one volt (1V) means that there is sufficient energy to give one electron an energy of one electronvolt.
As an electron moves through a potential difference, it experiences a change in energy:
- Higher potential corresponds to higher energy.

Question: Find the speed of a helium ion (He) when accelerated from rest through a potential difference of 12V.
Given Information:
- Helium ion (He) has 2 protons and an atomic mass of approximately 4 amu (atomic mass units).
- Initial speed (V_initial) = 0 m/s
- Potential difference (V) = 12V
Calculation Steps:
1. Calculate the energy gained using the formula:
- E = q * V
- q for He = 2 * (1.6 x 10^-19 C) = 3.2 x 10^-19 C (because He has two protons)
- Thus, E = 3.2 x 10^-19 C * 12V = 3.84 x 10^-18 joules
1. Relate kinetic energy (KE) to potential energy (PE):
- Since the helium ion starts from rest, all the gained potential energy converts into kinetic energy:
  - KE = PE
  - KE = E, hence, KE = 3.84 x 10^-18 joules

Kinetic energy (KE) can also be expressed as:
- KE = (1/2)mv^2
Where:
- m is the mass of the helium ion (approximately 6.64 x 10^-27 kg)
- v is the final velocity we want to determine.

In relation to kinetic energy and potential energy:
- PE = mgh where g is acceleration due to gravity.
In this context, it’s important to understand that potential energy can convert to kinetic energy and affects motion depending on external forces like gravity and electric fields.