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)
Continuous vs. Line Spectra
Quantised Energy Levels
The existence of sharp, discrete lines (not a continuous rainbow) proves that electron transitions occur only between fixed, discrete energy levels within atoms.
Calculate Frequency from Wavelength
Problem: Red light has a wavelength of 700 nm. Calculate its frequency.
1. Convert Units: \(\lambda\) must be in metres: \(700\text{ nm} = 700 \times 10^{-9}\text{ m} = 7.00 \times 10^{-7}\text{ m}\).
2. Rearrange Wave Equation: \(\nu = \dfrac{c}{\lambda}\)
3. Substitute Values: \(\nu = \dfrac{3.00 \times 10^8\text{ m s}^{-1}}{7.00 \times 10^{-7}\text{ m}} = \mathbf{4.29 \times 10^{14}\text{ Hz}}\)
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