I know what the actual number is, and when to use it (in equations), but where did it come from? And what is a “joule second?”
Max Planck was working on how radiation is related to temperature. After studying this for awhile he came up with answers that only made sense if the energy of a given atom (or back then he was probably looking at molecules…I don’t know) were quantized. That is, they could only take on certain values and not any values in between the allowable values. After a bit more work he derived the Planck Constant (which he personally thought was a mathematical fudge at the time).
A joule is 1 kg m[sup]2[/sup]/sec[sup]2[/sup]. Another way to think about a joule is angular momentum (I think…at least I remember my physics prof. saying that once but I’m no expert).
Actually, what happened is that in blackbody radiation (or cavity radiation), classical models predict an ultraviolet divergence in the power spectrum, while experiment begged to differ. Planck found that by assuming energy was quantized in terms of the frequency with the constant that bears his name, he could fix everything.
The Joule-second is just a particular combination of units that shows up a lot in quantum mechanics. It’s energytime, positionmomentum, angular momentum, and so on. Don’t worry about it too much, is my advice; anyone who has to use Planck’s constant a lot sets it equal to dimensionless 1 anyway.
While it is true that both Energy and Angular momentum have the units N x m[sup]*[/sup], Energy is the scalar product of force x length, while Angular Momentum is the vector product of force x length.
The unit is the same, but the interpretation is different.
Plancks constant is basically ‘energy / frequency’, i.e. J/Hz, i.e. (kg x m[sup]2[/sup] / s[sup]2[/sup]) / (s[sup]-1[/sup]) == kg x m[sup]2[/sup] / s .
[sup]*[/sup]1Newton = 1kg * m / s[sup]2[/sup]
more precisely, energy is the scalar product of force x length, and torque is the vector product. Angular momentum is the vector product of linear momentum and length.
That’s it.
If we discover that light (& EM) is quantized into photons, and we propose that photons carry a certain amount of energy, how much does each photon carry? The higher the frequency of the corresponding wave, the higher the energy in each photon. Measuring energy per Hz gives Planck’s constant, so in one sense the photons are little else but little “Planck’s constant hunks” flying around.