# When using Planck's constant, how do I know when to use electron volts or joules?

Planck's constant may be written as 6.63 x 10^-34 Js or 4.14 x 10^-15 eVs right? But how do I choose which one I should use to figure out an answer to a question?

• well that just depends on the units you're using for your other quantities, and the units in which you want to express your result.. How do you know whether to use m/s or km/h in a mechanics problem? – user2723984 Jul 31 at 8:24

Your question is not primarily about Planck's constant, but about the meaning and use of units in physics. That is where you should focus your intellectual energy in order to resolve this question. You may think you are familiar with units, but I think your question suggests you should try to become even more familiar.

I would recommend you first return to some very simple examples of units, and then gradually generalize until you have really 'got' it, where I mean understood it fully, to the point where your intuition and instincts align with your reasoning faculty.

So a simple example would be buying bananas. Suppose, for the sake of argument, that the supermarket sells bananas in groups of 5. It is arranged that every bunch of bananas has 5 bananas. Then we can measure the number of items of fruit either in bananas or in bunches.

1 banana = 0.2 bunches
12 bananas = 2.4 bunches
2 bunches = 10 bananas
etc.

Your question about Planck's constant is like someone giving you a box of fruit and asking for calculations involving the contents of the box, and you are asking "should I use bananas or bunches when doing calculations and reporting results?" The answer is that you use whichever is more convenient.

But since energy is less familiar than items of fruit, I'll write a bit more in order to work up to the example of electron-volts.

We might go next to other familiar examples such as distance which can be measured in metres, miles, inches, millimetres etc., and time which can be measured in seconds, hours, nanoseconds etc. I am sure all this is reasonably familiar. From these one can construct units of velocity---not just the familiar metres per second and miles per hour, but also all other combinations such as inches per year and things like that. The point is that although the conversion factors are often real numbers rather than simple ratios of integers, all this involves fundamentally the same idea as my original example of bananas and bunches.

Now we come to electron-volts. The first thing is to be clear that the electron-volt is a unit of energy. It is not a charge or a voltage or a time or a banana but an energy. Then by using the definition (the first line below) one can begin to work with it:

$$\begin{array}{rcl} 1 \mbox{ electron-volt} &=& 1.60218 \times 10^{-19} \mbox{ joules}\\ 12 \mbox{ electron-volt} &=& 12 \times 1.60218 \times 10^{-19} \mbox{ joules} \\ &=& 1.92261 \times 10^{-18} \mbox{ joules} \\ 1 \mbox{ joule} &=& 6.24151 \times 10^{18} \mbox{ electron-volts}\\ etc. \end{array}$$

Finally, I will offer some advice in order to minimise the chance of making mistakes.

1. Because SI units are familiar, it is often helpful just to put everything in SI units during a calculation, and then convert to whatever other units you like right at the end.
2. However, this is not always the best policy. I think we each discover, by calculation of many examples, when the use of some other units becomes more convenient.
3. Whenever a group of factors in an equation gives an overall result which is dimensionless, then you can calculate that group on its own using whatever units you find convenient.

When in doubt always use SI units (or SI derived units). Then one can plug the values in the formula and gets the correct result in SI units (or the SI derived unit corresponding to the physical quantity).

The SI units for the Planck constant is Js.

The other form (with eVs) is there for convenience and can be used if one tracks the units. E.g. the energy frequency relation

$$E = h \nu$$

will then give $$E$$ in units of $$eV$$ instead of $$J$$ (the SI unit). The unit eV exists because when working with optical photons the numeric values for the photon energy in eV are numbers in the order of $$1$$ which is more convenient to work with.