Notes on Electronvolt and Potential Energy

Electronvolt (eV)

• 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

Potential Difference and Energy

• 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.

Problem Example: Helium Ion Acceleration

• 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 Equation

• 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.

Gravitational Potential Energy (Related Concept)

• 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.