Waves and optics

De Broglie wavelength - formula in LaTeX

The wavelength associated with a moving particle. The product in the denominator is the momentum, hence the equivalent form with p. Written this way, the formula holds for speeds much lower than the speed of light.

\lambda = \dfrac{h}{mv}

LaTeX code

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$$
\lambda = \dfrac{h}{mv}
$$

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What the symbols mean

$\lambda$: matter wavelength (m)
$h$: Planck constant, 6.626·10⁻³⁴ J·s
$m$: mass of the particle (kg)
$v$: speed of the particle (m/s)

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

Worked example

An electron moving at 10⁶ m/s has a matter wavelength of about 0.73 nm, comparable to the spacing of atoms in a crystal, which is why it diffracts on one. The unit product J·s can be written with a thin space, \mathrm{J\,s}, instead of a dot.

\lambda = \dfrac{6.626\cdot 10^{-34}\,\mathrm{J\,s}}{9.11\cdot 10^{-31}\,\mathrm{kg} \cdot 10^{6}\,\mathrm{m/s}} \approx 7.27\cdot 10^{-10}\,\mathrm{m}

LaTeX commands in this formula

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

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
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