askvity

How do you calculate the energy of an electron in a Bohr orbit?

Published in Atomic Energy 3 mins read

The energy of an electron in a Bohr orbit can be calculated using a specific formula that relates the energy level to the orbit number.

Calculating Electron Energy in Bohr Orbits

The energy of an electron in the nth Bohr orbit of a hydrogen atom is determined by the following formula:

E = -13.6/n² eV

Where:

  • E is the energy of the electron in electronvolts (eV).
  • n is the principal quantum number, which corresponds to the orbit number (n = 1, 2, 3, ...), with n=1 being the closest orbit to the nucleus.

Understanding the Formula

  • -13.6 eV: This is the energy of an electron in the first Bohr orbit (n=1) of a hydrogen atom, also known as the ground state. It is the minimum energy an electron in a hydrogen atom can have. The negative sign indicates that the electron is bound to the nucleus.
  • n²: The energy is inversely proportional to the square of the orbit number. This means that as the electron moves to higher orbits (larger n values), the energy becomes less negative (closer to zero), indicating that it requires less energy to remove the electron from the atom.

Examples of Bohr Orbit Energy Calculations

Here's how you can use the formula to calculate electron energies in various Bohr orbits:

  1. First Bohr Orbit (n=1):

    • E = -13.6 / (1²) = -13.6 eV
    • This matches the reference value; the energy of the electron is -13.6 eV.

  2. Second Bohr Orbit (n=2):

    • E = -13.6 / (2²) = -13.6 / 4 = -3.4 eV
    • The electron has a higher energy in the second orbit, making it less tightly bound to the nucleus.

  3. Third Bohr Orbit (n=3):

    • E = -13.6 / (3²) = -13.6 / 9 ≈ -1.51 eV
    • As n increases, the energy gets less negative (closer to zero)

Key Points

  • The energy levels are quantized, meaning electrons can only occupy specific energy levels corresponding to Bohr orbits.
  • The negative sign indicates the electron is bound to the nucleus.
  • As n increases (higher orbits), the energy required to remove the electron from the atom decreases.

Practical Implications

Understanding the energy of electrons in Bohr orbits is crucial in:

  • Spectroscopy: Analyzing light emitted or absorbed by atoms to determine electron transitions between energy levels.
  • Atomic Physics: Understanding the fundamental structure and behavior of atoms.
  • Quantum Chemistry: Studying chemical bonds and molecular properties.

Related Articles