# Why is light wavelength measured in nm?

Of course you can convert it into metres if you wished, but photon energy is measured as such:

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

In this scenario, Energy is measured in electron volts. But if we measured light in metres, wouldn't we get joules since we are using SI units? However, when converting between $$eV$$ and $$J$$ it's not a matter of place value, i.e one isn't $$\times10^n$$. What's causing this?

## 2 Answers

But if we measured light in metres, wouldn't we get joules since we are using SI units?

Of course we would get joules. It's the SI unit of energy. But in atomic physics one often uses a custom unit, for convenience, and this unit is just what it's called: electron [charge times] volt (by charge we mean its absolute value). If you do the calculation, you'll get

\begin{align} 1\,\mathrm{eV}&=1.602176634\times 10^{-19}\,\mathrm{C}\cdot\mathrm{V}=\\ &=1.602176634\times 10^{-19}\,\mathrm{J}. \end{align}

• I expect it's an issue with my maths, but could you show the steps of the equation. I thought it would lead to electon volts=1e-19 joules – yolo Jan 16 at 20:06
• @yolo don't forget that charge is also a dimensionful quantity, namely, its SI unit is coulomb. The product of coulomb and volt is joule. – Ruslan Jan 16 at 20:08
• perhaps dimensionful quantities are the crux of what I'm confused about. How do units work with respect with this – yolo Jan 16 at 20:15

It isn't always measured in nm. Why would you think that? We often pick units to make the number easier to handle, e.g. bring the typical measurements in to the range of 1's, 10's 100's which people can comprehend. Visible light is in the range of 100's of nm, and the size of an atom approximately 0.1 nm. And we ID elements, and bonds in compounds, from the emission/absorption spectra. Rather than say we have a line a 0.00000...5 m it makes more sense to say 500 nm. Not sure what other motive there is.