Quantisation of Energy: Energy Levels, Spectra, and Electromagnetic Radiation

Quantisation of Energy

Introduction

The concept of quantisation of energy is fundamental to understanding atomic structure and the behavior of electrons in atoms. It explains how electrons occupy discrete energy levels and how transitions between these levels result in the absorption or emission of electromagnetic radiation.

Energy Levels

Electron Shells and Energy Quantisation

• Energy Level: Each electron shell in an atom corresponds to a fixed quantity of energy. Electrons occupying a shell possess the same energy, defining the shell as an energy level.

• Transitions: Electrons can move between energy levels by absorbing or emitting energy, typically in the form of light (photons).

• Ground State: The lowest possible energy level where electrons reside is called the ground state.

• Excited State: When electrons occupy higher energy levels than the ground state, the atom is said to be in an excited state.

Example: In a hydrogen atom, the electron in the n=1 shell is in the ground state; if it absorbs energy, it may move to n=2 or higher, entering an excited state.

Excited State

Nature and Behavior of Excited States

• Atoms become excited when they absorb energy, such as from heat or light.

• The excited state is typically unstable and lasts only a fraction of a second.

• When the atom returns to its ground state, it emits the absorbed energy as a photon.

Example: An electron in hydrogen absorbs energy and jumps from n=1 to n=2 (excited state), then emits a photon as it returns to n=1.

Electromagnetic Radiation

Visible Light and Energy

• Electromagnetic Radiation: Energy that travels in waves and includes visible light, ultraviolet, infrared, and more.

• Each color of visible light is characterized by a specific wavelength, frequency, and energy.

Equation: The energy of a photon is given by $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency.

Example: Blue light has a higher frequency and energy than red light.

Absorption Spectra

Absorption of Energy and Electron Transitions

• Electrons jump to higher energy levels if they absorb the exact amount of energy corresponding to the difference between two levels.

• Electrons can jump one or multiple shells but cannot exist between shells.

Equation: The energy difference between levels is $\Delta E = E_{high} - E_{low}$.

Example: In hydrogen, absorption of a photon with energy matching the gap between n=1 and n=2 causes the electron to jump to n=2.

Absorption Spectrum and Absorption Lines

• When exposed to a continuous spectrum of light, an element absorbs only the wavelengths that match the energy needed for electron transitions.

• The absorbed wavelengths appear as absorption lines in the spectrum.

• Collectively, these lines form the absorption spectrum of the element.

Example: The absorption spectrum of hydrogen shows black lines at specific wavelengths where light is absorbed.

Emission Spectra

Emission of Energy and Electron Transitions

• When an atom is excited, its electrons move to higher energy levels. As they return to lower levels, they emit energy as photons.

• Emission can occur via different pathways: electrons may drop directly to the ground state or stepwise through intermediate levels.

• Each transition emits light of a specific frequency, corresponding to the energy difference between levels.

Equation: $E_{photon} = E_{initial} - E_{final}$

Example: The Balmer series in hydrogen emission spectrum corresponds to transitions ending at n=2.

Emission Lines and Emission Spectrum

• The individual colors of light emitted are called emission lines.

• All emission lines together form the emission spectrum of an element.

• Each element has a unique emission spectrum, useful for identification.

Example: Hydrogen's emission spectrum shows distinct colored lines at specific wavelengths.

Comparison: Emission vs Absorption

Key Differences

Process	Result	Spectrum Appearance
Absorption	Electrons absorb energy and move to higher levels	Dark lines on a continuous spectrum
Emission	Electrons emit energy as they return to lower levels	Bright lines on a dark background

Example: Hot gases produce emission spectra; cold gases in front of a light source produce absorption spectra.

Summary Table: Absorption vs Emission Spectra

Type	Cause	Appearance	Application
Absorption Spectrum	Electrons absorb photons and move to higher energy levels	Dark lines on a colored background	Identifying elements in stars
Emission Spectrum	Electrons emit photons as they return to lower energy levels	Colored lines on a dark background	Flame tests, spectroscopy

Additional Info

• These principles are foundational for analytical techniques such as UV-Vis spectroscopy and atomic absorption spectroscopy, which are used in organic and inorganic chemistry to identify and quantify substances.

• Quantisation of energy is a key concept in quantum mechanics and underpins the electronic structure of atoms and molecules.