Energy Levels in Atoms - Full Explanation
1. Introduction
In atomic physics, energy levels refer to the discrete values of energy that electrons can have in an
atom. These levels arise due to the quantization of energy, meaning electrons cannot have arbitrary
energies but must exist in fixed states. The concept of energy levels helps explain various atomic
properties, such as spectral lines, ionization, and chemical bonding.
2. Energy Levels and Electron Orbits
Electrons in an atom revolve around the nucleus in specific energy levels or shells. These energy
levels are represented by principal quantum numbers (n = 1, 2, 3, ...). Lower energy levels (smaller
n) are closer to the nucleus, while higher energy levels (larger n) are farther from the nucleus and
have higher energy.
3. Energy Quantization and the Bohr Model
According to Bohr's atomic model, the energy of an electron in the nth energy level of a hydrogen
atom is given by:
E_n = - (13.6 eV) / n^2
where:
- E_n = energy of the electron in the nth orbit
- 13.6 eV = ionization energy of hydrogen
- n = principal quantum number (1, 2, 3, ...)
Higher n-values have less negative energy, meaning electrons are less tightly bound. If an electron
gains enough energy (13.6 eV or more), it can escape the atom, leading to ionization.
4. Electron Transitions and Photon Emission
Electrons can move between energy levels by absorbing or emitting energy. When an electron
absorbs a photon, it jumps to a higher energy level. When an electron falls to a lower energy level, it
emits a photon of a specific wavelength. The energy difference between two levels is given by
Planck's equation:
E=hf
where:
1. Introduction
In atomic physics, energy levels refer to the discrete values of energy that electrons can have in an
atom. These levels arise due to the quantization of energy, meaning electrons cannot have arbitrary
energies but must exist in fixed states. The concept of energy levels helps explain various atomic
properties, such as spectral lines, ionization, and chemical bonding.
2. Energy Levels and Electron Orbits
Electrons in an atom revolve around the nucleus in specific energy levels or shells. These energy
levels are represented by principal quantum numbers (n = 1, 2, 3, ...). Lower energy levels (smaller
n) are closer to the nucleus, while higher energy levels (larger n) are farther from the nucleus and
have higher energy.
3. Energy Quantization and the Bohr Model
According to Bohr's atomic model, the energy of an electron in the nth energy level of a hydrogen
atom is given by:
E_n = - (13.6 eV) / n^2
where:
- E_n = energy of the electron in the nth orbit
- 13.6 eV = ionization energy of hydrogen
- n = principal quantum number (1, 2, 3, ...)
Higher n-values have less negative energy, meaning electrons are less tightly bound. If an electron
gains enough energy (13.6 eV or more), it can escape the atom, leading to ionization.
4. Electron Transitions and Photon Emission
Electrons can move between energy levels by absorbing or emitting energy. When an electron
absorbs a photon, it jumps to a higher energy level. When an electron falls to a lower energy level, it
emits a photon of a specific wavelength. The energy difference between two levels is given by
Planck's equation:
E=hf
where:
