Difference Between Continuous and Discrete Spectrum

The key difference between continuous and discrete spectrum is that a continuous spectrum does not have any discrete lines, whereas a discrete spectrum contains only discrete lines.

The terms continuous spectrum and discrete spectrum are the opposite of each other. A spectrum can be created using the values obtained for a certain physical quantity. The presence or absence of gaps between these values can create a discrete or a continuous spectrum, respectively.

1. Overview and Key Difference
2. What is Continuous Spectrum
3. What is Discrete Spectrum
4. Side by Side Comparison – Continuous vs Discrete Spectrum in Tabular Form
5. Summary

What is Continuous Spectrum?

A continuous spectrum is a series of attainable values of a physical quantity, having no considerable gap between each value. This value series is the opposite of the discrete spectrum. The values taken to build up a continuous spectrum can be energy, wavelength, etc.

The most common example for a continuous spectrum is the spectrum of the light emitted by excited atoms of hydrogen. This spectrum is created due to free electrons, which become bound to a hydrogen ion and emit photons that tend to smoothly spread over a wide range of wavelengths.

The term continuous spectrum is mostly used when the range of values for the physical quantity (mainly energy or wavelength) have both continuous and discrete parts, either at the same time or at different times. This is because the position and momentum of a free particle have a continuous spectrum, and when the particle is confined to limited space, its spectrum becomes a discrete spectrum. Usually, quantum chemical systems are associated with free particles (e.g. atoms in a gas, electrons in an electron beam, conduction band electrons in a metal, etc.).

What is Discrete Spectrum?

A discrete spectrum is a series of attainable values of a physical quantity having a positive gap between each value. This is opposite to the continuous spectrum. This type of spectrum occurs due to electrons falling from some bound quantum state to a lower energy state.

Difference Between Continuous and Discrete Spectrum

Figure 01: Comparison of Continuous and Discrete Spectra (Emission and Absorption Lines are Examples of Discrete Spectra)

Generally, quantum chemical systems have discrete spectra that are usually associated with free particles; thus, the position and momentum of a free particle are confined to a limited space, which results in a discrete spectrum.

What is the Difference Between Continuous and Discrete Spectrum?

A continuous spectrum is a series of attainable values of a physical quantity, with no considerable gap between each value. A discrete spectrum is a series of attainable values of a physical quantity, having a positive gap between each value. The key difference between continuous and discrete spectrum is that a continuous spectrum does not have any discrete lines, whereas a discrete spectrum contains only the discrete lines. Therefore, a continuous spectrum is a continuous series while a discrete spectrum has separate lines or values. Moreover, a spectrum of a glowing object is an example of a continuous spectrum while the absorption or emission spectrum of isolated atoms of a chemical element is an example of a discrete spectrum.

The below infographic shows the differences between continuous and discrete spectrum in tabular form.

Summary – Continuous vs Discrete Spectrum

Continuous spectrum and discrete spectrum are usually considered the opposite of each other. The key difference between continuous and discrete spectrum is that a continuous spectrum does not have any discrete lines, whereas a discrete spectrum contains only the discrete lines.