When atoms absorb energy, their electrons jump to higher energy levels (excited state). As they fall back to lower, more stable energy levels, they emit energy in the form of photons of light. This emitted light creates an emission spectrum.
1. Wave Equation
\( c = \nu \lambda \)
c = Speed (\(3.00 \times 10^8\) m/s)
ν = Frequency (Hz or s⁻¹)
λ = Wavelength (m)
2. Photon Energy
\( E = h \nu \)
E = Energy (Joules)
h = Planck (\(6.63 \times 10^{-34}\))
ν = Frequency (Hz)
How Emission Works
Continuous vs. Line Spectra
The existence of sharp, discrete lines (not a continuous rainbow) proves that electrons can only exist at fixed, quantized energy levels. If energy levels were continuous, we would see a smooth rainbow instead of distinct lines.
Calculate Frequency from Wavelength
Problem: Red light has a wavelength of 700 nm. Calculate its frequency.
1. Convert Units: λ must be in meters.
\( 700 \text{ nm} = 700 \times 10^{-9} \text{ m} \)
2. Rearrange Formula: \( c = \nu \lambda \rightarrow \nu = c / \lambda \)
3. Solve:
\( \nu = \frac{3.00 \times 10^8}{700 \times 10^{-9}} \)
\( \nu = 4.29 \times 10^{14} \text{ Hz} \)