Hydrogen Emission Spectrum

The hydrogen atom has only one electron. When it absorbs energy, the electron moves to a higher energy level (excited state). When the electron returns to a lower energy level, it emits energy in the form of light (a photon).

This emitted light appears as a line spectrum a series of discrete lines at specific wavelengths, providing evidence that electrons exist in quantised energy levels.

Spectral Series in Hydrogen:

• Lyman series: transitions to \( n = 1 \) (ultraviolet region)
• Balmer series: transitions to \( n = 2 \) (visible region)
• Paschen series: transitions to \( n = 3 \) (infrared region)

Concepts:

• Each line in the emission spectrum corresponds to an electron transition from a higher to a lower energy level.
• Lines converge (get closer together) at higher energies – this is due to energy levels getting closer as \( n \) increases.
• The shortest wavelength (highest frequency) line corresponds to the largest energy transition.

Interpretation:

• Lines in the UV region (Lyman series) involve transitions with larger energy differences → higher energy photons.
• Lines in the visible region (Balmer series) correspond to transitions like \( n = 3 \rightarrow 2 \), \( n = 4 \rightarrow 2 \), etc.
• Lines in the infrared region (Paschen series) involve smaller energy changes → lower energy photons.

Evidence for Quantisation:

• The presence of discrete lines (not a continuous spectrum) confirms that electrons can only occupy certain allowed energy levels.
• As \( n \rightarrow \infty \), the levels converge indicating ionisation limit (electron completely removed).

Formula for Energy Transitions:

\( \Delta E = E_{\text{high}} – E_{\text{low}} = hf = \frac{hc}{\lambda} \)

Where \( h \) is Planck’s constant and \( c \) is the speed of light.