# A question about plank constant

1. Oct 16, 2009

### pixel01

A young student asks me "why mr. Max Planck could find out the planck constant. How come he could find such a small number (the planck constant ~ 6.62 E-34). Anyone could help me to explain to the boy?
thanks

2. Oct 16, 2009

### keniwas

Plancks constant originally came about as a numerical approximation to a fit constant. Planck was trying to explain the blackbody radiation spectrum. Using normal boltzmann statistics to try and explain the distribution of energy, he made the postulate that the energy could only come in discrete packets of energy proportional to $$h\nu$$ where $$\nu$$ was the frequency of the electromagnetic radiation and h was some constant scaling factor. So to make a long story short, he was left with a distribution of the form
$$I(\nu,T)=\frac{2h\nu^3}{c^2}\frac{1}{e^{\frac{h\nu}{kT}}-1}$$

Where everything was known except the constant h. By what essentially amounted to a series of least squares fitting, he was able to find the constant h that worked for all distributions at various temperatures T.

3. Oct 16, 2009

### f95toli

He fitted his experssion to experimental data, specifically data showing the frequency distribution of blackbody radiation from a source with a known temperature.

The fact that the constant is "small" doesn't matter when it comes to fitting data.

Edit: Keniwas was faster...

4. Oct 16, 2009

### keniwas

;) but now we have two posts that agree so it gives support that the answer is indeed correct.

5. Oct 16, 2009

### Bob_for_short

The numerical value of h depends on units, so it may be made unity in the Plank or other units.

6. Oct 16, 2009

### Count Iblis

The fact that Planck's constant is dimensionful and the fact that it is not of order unity when expressed in the everyday units, are linked.

It turns out that that Length, Time, and Mass are not independent but that they are related. But these relationships are effectively invisible to classical physicists. The classical physicists thought that you could never compare a length to a time interval and a mass to a length or a time interval, i.e. that the units for mass, time and length must be fundamentally incompatible. That's why these units were assigned incompatible dimensions.

This later turned out to be wrong. Relations between the units were found. Because we decided not to correct our error and keep the incompatible dimensions for the units, the constants hbar, c, and G that relate the units get dimensions.

7. Oct 17, 2009

### pixel01

Thanks to all for explanation.