The Electromagnetic Spectrum (HSC SSCE Physics): Revision Notes

The Electromagnetic Spectrum

Introduction

The electromagnetic spectrum is the complete range of electromagnetic radiation, organized by frequency and wavelength. Understanding how light behaves in different materials and how atoms interact with light helps us identify elements and understand the nature of electromagnetic radiation.

Refractive index

Light travels at different speeds in different materials. In a vacuum, light travels at its maximum speed of $c = 3.00 \times 10^8$ m/s. However, when light enters a material such as water or glass, it slows down due to interactions with the atoms in the material.

The refractive index ($n$) measures how much a material slows down light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material:

$n = \frac{c}{v}$

where:

• $n$ is the refractive index (no units)
• $c$ is the speed of light in a vacuum ($3.00 \times 10^8$ m/s)
• $v$ is the speed of light in the material (m/s)

Refractive indices of common materials

The following table shows how different materials affect the speed of light:

Material	Refractive index
Air	1.0003
Water	1.33
Ethanol	1.36
Zircon	1.92
Diamond	2.42

Notice that diamond has the highest refractive index among common materials, meaning light travels slowest in diamond - only about 41% of its vacuum speed.

Dispersion

The refractive index of a material actually varies with the wavelength of light. This means different colours of light travel at slightly different speeds in the same material and refract by different amounts.

When white light passes through a prism or water droplet, this variation causes the different colours to separate and spread out. This phenomenon is called dispersion. It is responsible for creating rainbows and the coloured spectrum we see when white light passes through a prism.

The electromagnetic spectrum

When electromagnetic radiation is arranged by frequency or wavelength, we get the electromagnetic spectrum. This spectrum includes all types of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays.

Types of electromagnetic radiation

The electromagnetic spectrum includes (from lowest to highest frequency):

1. Radio waves - Longest wavelengths (kilometres to metres). Used for radio and television broadcasting. Frequencies from $10^3$ to $10^9$ Hz.
2. Microwaves - Wavelengths of centimetres to millimetres. Used in microwave ovens and satellite communications. Frequencies around $10^9$ to $10^{12}$ Hz.
3. Infrared radiation - Wavelengths from about 1 mm to 700 nm. Felt as heat. Used in thermal imaging and remote controls. Frequencies from $10^{12}$ to $10^{14}$ Hz.
4. Visible light - The only part of the spectrum our eyes can detect. Wavelengths from about 400 nm (violet) to 700 nm (red). Frequencies from $10^{14}$ to $10^{15}$ Hz. This narrow band contains all the colours we see: red, orange, yellow, green, blue, and violet.
5. Ultraviolet (UV) radiation - Wavelengths shorter than visible light, from about 400 nm down to 1 nm. Can cause sunburn. Frequencies from $10^{15}$ to $10^{17}$ Hz.
6. X-rays - Very short wavelengths (1 nm to 1 pm). Used in medical imaging and security scanning. Frequencies from $10^{17}$ to $10^{20}$ Hz.
7. Gamma rays - Shortest wavelengths (less than 1 pm). Produced by radioactive materials and cosmic events. Frequencies above $10^{19}$ Hz.

The visible spectrum

The visible light portion of the spectrum is the narrow range that human eyes can detect. It extends from violet light (around 400 nm) to red light (around 700 nm). The colours in order of increasing wavelength are:

• Violet (shortest wavelength, ~400 nm)
• Blue
• Green
• Yellow
• Orange
• Red (longest wavelength, ~700 nm)

Spectral lines and identifying elements

Spectroscopy is the study of how electromagnetic radiation interacts with matter. It has become one of the most powerful tools in science, allowing us to identify elements in stars, distant galaxies, and laboratory samples.

Historical development

In 1802, English physician William Wallace Hyde noticed dark lines in the Sun's spectrum. German physicist Joseph von Fraunhofer catalogued about 500 of these lines in 1814 and found that the spectrum of Venus matched that of the Sun. He also observed spectra from many stars.

From around 1848, scientists including Foucault, Bunsen, and Kirchhoff identified various solar spectral lines with the known emission lines of different elements. This proved that the same elements found on Earth also exist in the Sun and other stars.

The photon model of light

To understand spectral lines, we need to think of light as consisting of particles called photons. Each photon carries a specific amount of energy related to its frequency by the equation:

$E = hf$

where:

• $E$ is the photon energy (in joules or electron volts)
• $h$ is Planck's constant ($6.63 \times 10^{-34}$ J·s)
• $f$ is the frequency (in Hz)

Since frequency and wavelength are related by $f = \frac{c}{\lambda}$, we can also write:

$E = \frac{hc}{\lambda}$

Electron energy levels

Every electron in an atom occupies a specific energy level or shell. The lowest energy level is called the ground state. Electrons in the ground state are stable and do not radiate energy.

However, if a photon with exactly the right energy interacts with an electron, the electron can absorb that energy and jump to a higher energy level. The electron is then in an excited state, which is unstable.

The excited electron will eventually fall back down to a lower energy level, releasing the absorbed energy as a photon. The energy of this emitted photon exactly equals the energy difference between the two levels.

Absorption and emission spectra

There are two types of line spectra we can observe:

Absorption lines: When white light from an incandescent source (like a hot filament or star) passes through a cool gas, atoms in the gas absorb photons at specific frequencies. These missing frequencies appear as dark lines in an otherwise continuous spectrum. The atoms absorb photons that have exactly the right energy to promote their electrons to higher energy levels.

Emission lines: When we view a sample of excited gas atoms from an angle (not looking at the background source), we see bright coloured lines on a dark background. These emission lines are produced when excited electrons fall back to lower energy levels and emit photons in random directions.

Incandescent sources

An incandescent source is one that produces light by being heated, such as:

• A tungsten filament in a light bulb
• The surface of a star
• A hot metal object

Incandescent sources produce a continuous spectrum containing all wavelengths, with the peak wavelength depending on temperature. Hotter objects emit more blue light, while cooler objects emit more red light. Our Sun appears white because its peak wavelength is in the green region, but it emits significant amounts of blue light as well, which our brain interprets as white.

The Balmer series

The Balmer series refers to a specific set of visible emission lines from hydrogen. These lines are produced when excited electrons fall from higher shells down to the second shell ($n = 2$).

Transition	Colour	Wavelength (nm)
3 → 2	Red	656.3
4 → 2	Aqua	486.1
5 → 2	Blue	434.1
6 → 2	Violet	410.2

These are the main visible spectral lines of hydrogen and are easily observed in laboratory experiments and astronomical observations.

Investigation: Visible spectral lines

Aim

To examine various spectra produced by discharge tubes, reflected sunlight, and incandescent filaments.

Materials

• Hand-held spectroscope
• Induction coil
• 12V incandescent globe
• 12V power supply
• Leads and alligator clips
• Discharge tubes containing different gases (sodium, mercury)

Risk assessment

Method

1. Set up the induction coil and discharge tubes in a darkened room.
2. Observe the spectrum produced by each discharge tube using the hand-held spectroscope. Sketch your observations, noting the colours and positions of the emission lines.
3. Observe the spectrum produced by a fluorescent light and compare it with those from the discharge tubes. Note similarities and differences.
4. Connect the 12V incandescent globe to the power supply. Observe its spectrum without other light sources present. Try different voltage settings and note how changes in temperature affect both the intensity and the range of colours produced.
5. Go outside and observe the spectrum from reflected sunlight using a white wall. Ensure the spectroscope is carefully focused. Compare this with the other spectra you observed.

Expected observations

• Discharge tubes: You should see bright emission lines at specific wavelengths, unique to each gas. Mercury, for example, produces distinct violet, blue, green, yellow, and red lines.
• Fluorescent light: Similar to discharge tubes, showing emission lines from the mercury vapour inside.
• Incandescent globe: A continuous spectrum containing all colours. As voltage (and temperature) increases, the light becomes brighter and whiter as more blue light is produced.
• Sunlight: A continuous spectrum with dark absorption lines (Fraunhofer lines) where elements in the Sun's atmosphere have absorbed specific wavelengths.

Discussion

The differences between these spectra demonstrate:

• Incandescent sources produce continuous spectra
• Gas discharge tubes produce line emission spectra characteristic of the element
• The Sun's spectrum shows both continuous and absorption features