Waves and optics

Photon energy - formula in LaTeX

The energy of a single quantum of light. The Greek letter nu (\nu) looks almost like v, which makes them easy to confuse in handwritten notes; in LaTeX they are two different characters, so check which one you typed.

E = h\nu = \dfrac{hc}{\lambda}

LaTeX code

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$$
E = h\nu = \dfrac{hc}{\lambda}
$$

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What the symbols mean

$E$: photon energy (J)
$h$: Planck constant, 6.626·10⁻³⁴ J·s
$\nu$: frequency (Hz)
$c$: speed of light, 3.00·10⁸ m/s
$\lambda$: wavelength (m)

A waves and optics formula - common in interference, refraction and quantum physics problems.

Worked example

A photon of green light with a 500 nm wavelength carries about 3.98·10⁻¹⁹ J, or 2.48 eV. Nanometres become metres through the factor 10^{-9}, and multiplication in scientific notation is written \cdot (English texts often use \times).

E = \dfrac{hc}{\lambda} = \dfrac{6.626\cdot 10^{-34}\,\mathrm{J\,s} \cdot 3.00\cdot 10^{8}\,\mathrm{m/s}}{500\cdot 10^{-9}\,\mathrm{m}} \approx 3.98\cdot 10^{-19}\,\mathrm{J}

LaTeX commands in this formula

\nu: Greek letter nu
\dfrac: fraction (display)
\lambda: Greek letter lambda

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
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Inside a sentence, use single $…$ instead of double.
The formula needs the amsmath package - CamteX templates include it in the preamble.

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