Spectra (HSC SSCE Physics): Revision Notes

Spectra

Spectra are patterns of light that help us understand the structure of atoms. Different elements produce unique spectral patterns that act like fingerprints, allowing scientists to identify elements. This note focuses on the hydrogen spectrum, which provided crucial evidence for understanding atomic structure.

What are spectra?

A spectrum (plural: spectra) is the pattern of light separated into its component wavelengths. There are three main types:

• Emission spectrum: bright coloured lines on a dark background, produced when excited atoms emit light at specific wavelengths
• Absorption spectrum: dark lines on a continuous coloured background, created when atoms absorb specific wavelengths from white light
• Continuous spectrum: an unbroken band of all colours, produced by hot solid objects or dense gases

Observing spectra using gas discharge tubes

When electrical energy passes through a gas at low pressure inside a glass tube, the gas glows with a characteristic colour. This device is called a gas discharge tube.

Different elements produce distinctly different colours when energised in this way:

• Helium produces a pinkish-orange glow
• Neon glows bright orange-red (familiar from "neon lights")
• Argon appears blue-violet
• Krypton emits a whitish-blue light
• Xenon produces a blue-white glow

Investigation 15.1: Observing spectra

This practical investigation allows you to observe and photograph the emission spectrum of hydrogen gas.

Aim

To observe and photograph the emission spectrum of hydrogen.

Materials

• Hand-held spectroscope
• Hydrogen gas discharge tube
• Induction coil or similar high-voltage apparatus
• 12V power pack
• Alligator leads
• Darkened room/laboratory
• Suitable camera (such as a mobile phone)

Safety considerations

Method

1. Connect the hydrogen discharge tube to the induction coil and 12V power pack. Ensure the power remains disconnected whilst handling the apparatus.
2. Switch on the power and observe the spectrum produced by the hydrogen through the hand-held spectroscope.
3. Carefully align the camera lens with the eyepiece of the spectroscope and photograph the spectrum you observe.

Results

When you look through the spectroscope at the hydrogen discharge tube, you will observe a pattern of discrete bright coloured lines against a dark background. These lines appear at specific wavelengths in the visible region of the spectrum.

Discussion points

Why is this an emission spectrum?

This is classified as an emission spectrum because the hydrogen atoms are emitting light at specific wavelengths, producing bright lines on a dark background. The atoms absorb electrical energy, become excited, and then release this energy as light photons of particular wavelengths.

What mechanism produces this spectrum?

The hydrogen spectrum

Hydrogen is the simplest element, containing just one electron. This makes it ideal for studying atomic structure. When hydrogen gas is excited in a discharge tube, it produces spectral lines in three regions of the electromagnetic spectrum: ultraviolet, visible, and infrared.

Emission and absorption spectra

The hydrogen spectrum can be observed in two forms:

The emission spectrum (top) shows bright coloured lines at specific wavelengths on a dark background. These represent the wavelengths of light emitted by excited hydrogen atoms.

The absorption spectrum (bottom) displays a continuous rainbow of colours with dark lines at specific wavelengths. These dark lines appear at exactly the same positions as the bright lines in the emission spectrum. When white light passes through cool hydrogen gas, the atoms absorb light at these specific wavelengths, creating the dark absorption lines.

Spectral series of hydrogen

Although scientists had observed spectral patterns, there was initially no theory explaining why they existed. It was presumed that these characteristic spectra related to the internal structure of atoms. Hydrogen, being the simplest atom, became the focus of intense investigation.

In 1855, Swiss mathematician Johann Balmer derived an empirical formula for the visible spectral lines of hydrogen. He discovered that the observed wavelengths were proportional to $\frac{m^2}{m^2 - n^2}$, where $n = 2$ and $m$ is greater than $n$. This series of visible lines is now called the Balmer series.

Further research revealed that hydrogen produces several series of spectral lines:

Additional series exist at even longer wavelengths: the Brackett series and Pfund series. All these series follow similar patterns but with different values for the initial ($n_i$) and final ($n_f$) energy levels.

Electron transitions and spectral lines

The spectral lines correspond to electron transitions between different energy shells in the hydrogen atom:

Each coloured arrow in the diagram represents an electron transition that produces a spectral line. The wavelength of the emitted light depends on the energy difference between the two levels:

• Lyman series (green arrows): electrons falling from higher levels ($n = 2, 3, 4...$) to the ground state ($n = 1$). These transitions involve the largest energy changes, producing ultraviolet photons with wavelengths from 94 nm to 122 nm.
• Balmer series (black arrows): electrons falling from higher levels ($n = 3, 4, 5...$) to $n = 2$. These intermediate energy changes produce visible light with wavelengths from 410 nm to 656 nm.
• Paschen series (magenta arrows): electrons falling from higher levels ($n = 4, 5, 6...$) to $n = 3$. These smaller energy changes produce infrared radiation with wavelengths from 1094 nm to 1875 nm.

The spacing between spectral lines within each series follows a pattern: the lines get closer together as the wavelength decreases, converging toward a series limit. This pattern provided crucial evidence for the quantised nature of atomic energy levels.