Photon Energy from Wavelength

📊 beginner

$$E = \frac{hc}{\lambda}$$

Energy of photon in terms of wavelength.

Variables & Units

$E$

Photon energy

Unit: $\text{J}$

$h$

Planck's constant

Unit: $\text{J·s}$

$c$

Speed of light

Unit: $\text{m/s}$

$\lambda$

Wavelength

Unit: $\text{m}$

Key Information

📐 Derived From

$E = h\nu$ and $c = \lambda\nu$

💡 Example

Blue light $\lambda = 450\,\text{nm} = 4.5\times10^{-7}\,\text{m}$: $E = (6.626\times10^{-34})(3\times10^8)/(4.5\times10^{-7}) = 4.42\times10^{-19}\,\text{J} = 2.76\,\text{eV}$.

🔧 Applications

Photovoltaics, LED design, spectroscopy

⚠️ Constraints

Vacuum or air (n≈1)

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