Atomic Line Spectra: Production of Absorption and Emission Spectra

Introduction

Atoms can absorb or emit photons of specific energies, leading to the production of atomic absorption and emission line spectra. These spectra provide crucial information about the composition and properties of matter.

Quantized Energy Levels

Electrons in atoms can only occupy specific energy levels, also known as quantized states.
* These energy levels are analogous to standing waves; only certain wavelengths (and thus energies) can exist without destructive interference.
* Electrons exist in specific orbitals, each associated with a discrete energy level.

KEY TAKEAWAY: Electron energy levels in atoms are quantized, meaning electrons can only occupy specific energy levels.

Emission Spectra

Production

Emission spectra are produced when excited atoms lose energy by emitting photons.
1. An atom is excited, meaning an electron jumps to a higher energy level. This can occur through heating or electrical discharge.
2. The excited electron spontaneously returns to a lower energy level.
3. As the electron transitions, it emits a photon with energy equal to the energy difference between the two levels.

Characteristics

• An emission spectrum consists of discrete, bright lines at specific wavelengths.
• Each element has a unique emission spectrum, acting as a “fingerprint.”

Formula

The energy of the emitted photon is given by:
$$E = hf = \frac{hc}{\lambda}$$
Where:
* $E$ = energy of the photon (J or eV)
* $h$ = Planck’s constant (\$6.63 \times 10^{-34} \text{ Js}$ or \$4.14 \times 10^{-15} \text{ eVs}$)
* $f$ = frequency of the photon (Hz)
* $c$ = speed of light (\$3.0 \times 10^8 \text{ m/s}$)
* $\lambda$ = wavelength of the photon (m)

Example

Consider an electron transitioning from energy level $E_2$ to $E_1$. The energy of the emitted photon is:
$$E = E_2 - E_1$$

EXAM TIP: Be comfortable converting between electron volts (eV) and Joules (J). Remember that \$1 \text{ eV} = 1.602 \times 10^{-19} \text{ J}$.

Absorption Spectra

Production

Absorption spectra are produced when light passes through a gas and the gas absorbs specific wavelengths of light.
1. White light (containing all wavelengths) passes through a cool gas.
2. Atoms in the gas absorb photons with energies that match the energy difference between their energy levels.
3. The absorbed photons cause electrons to jump to higher energy levels.

Characteristics

• An absorption spectrum consists of a continuous spectrum with dark lines at specific wavelengths.
• The dark lines correspond to the wavelengths of light that have been absorbed by the gas.
• The absorption spectrum of an element is unique and complementary to its emission spectrum.

Relationship to Emission Spectra

The wavelengths of the dark lines in an absorption spectrum are the same as the wavelengths of the bright lines in the corresponding emission spectrum.

COMMON MISTAKE: Confusing absorption and emission spectra. Remember that absorption spectra have dark lines on a continuous background, while emission spectra have bright lines on a dark background.

Metal Vapour Lamps

Function

Metal vapour lamps utilize the principle of atomic emission to produce light.
* A gas (e.g., sodium, mercury) is contained within a glass tube.
* An electric current is passed through the gas, exciting the atoms.
* The excited atoms then emit photons as their electrons transition to lower energy levels, producing light.

Examples

• Sodium vapour lamps: Emit a characteristic yellow light and are commonly used for street lighting.
• Mercury vapour lamps: Emit a bluish-white light and are used in industrial lighting and some streetlights.

Advantage of Metal Vapour Lamps

Metal vapour lamps are efficient at converting electrical energy into light, making them suitable for applications where energy conservation is important.

APPLICATION: Metal vapour lamps are used in street lighting because of their efficiency and characteristic emission spectra.

Electron Standing Waves and the Dual Nature of Matter

The concept of quantized energy levels can be explained by the wave nature of electrons.
* Electrons behave as waves and can form standing waves around the nucleus.
* Only specific electron orbitals can exist where the electron forms a standing wave, which is not always possible.
* The de Broglie wavelength ($\lambda = \frac{h}{p}$) relates the wavelength of an electron to its momentum ($p$).

STUDY HINT: Draw energy level diagrams to visualize electron transitions and the corresponding emission or absorption of photons.

Summary Table: Emission vs. Absorption Spectra

VCAA FOCUS: VCAA often asks about the relationship between energy level transitions and the wavelengths of light emitted or absorbed. Make sure you understand the formula $E = hf = \frac{hc}{\lambda}$ and how to apply it.