What is the Significance of Planck's Constant and its Reduced Form?

[nuby]

Hello,

After reading a little about Planck's constant, I'm a bit confused. The constant is measured in Joules * Sec, how is joules*sec converted into an actual size. Also, the reduced Planck's constant is

h/2pi

Why is this? h/2pi looks like it could be a Radius. Is the constant h and the reduced constant ever thought to be a radius and circumference (of quanta)?

 

[rohanprabhu]

how is joules*sec converted into an actual size.

actual size?? what exactly do you mean by that?

Also, the reduced Planck's constant is

h/2pi

Why is this? h/2pi looks like it could be a Radius. Is the constant h and the reduced constant ever thought to be a radius and circumference (of quanta)?

When we say 'Joules-sec', we can also state it as: 'Joules/Hz' since, frequency [measured in Hz] is dimensionally the reciprocal of time [measured in sec]. Planck, in the Planck's law of black-body radiation proposed that the electromagnetic radiation emitted by the black-body could be modeled as a set of harmonic oscillators, with quantized energy of the form:

$$E = h\nu$$

basically what Planck intends to say is that each photon i.e. the particle manifestation of light has energy proportional to it's frequency. Hence, the term 'Joules -per- Hertz'. The unit is equivalent of saying 'Energy per unit frequency'.

The 'reduced Planck constant', aka the 'Dirac constant' differs from the Planck constant by a factor of $2\pi$. When we discuss wave like phenomena, we also discuss cyclic parameters, like angular frequency, angular wavenumber, phase etc. All these parameters, for example the angular frequency, differs from the frequency by a factor of $2\pi$. Hence while writing the equations involving cyclic parameters, it is helpful if the Dirac constant is used. It is purely a matter of convenience.

 

[maverick_starstrider]

I think you may be confusing plank's constant with a plank length. a plank length = $$\sqrt{\frac{hG}{2 \pi c^3}} \approx 1.62 \cross 10^{-35}$$ meters which is a distance. Does that help?

 

[maverick_starstrider]

As for what plank's constant MEANs I suppose there's no better explanation than it's the amount of energy that a photon with a frequency of 1 Hz possesses. Or are you looking for something more metaphysical then that?

 

[nuby]

actual size?? what exactly do you mean by that?

By size i meant: if 'h' could ever be equated to a wavelength, and h/2pi a radius of an electromagnetic wave.

 

[maverick_starstrider]

well since $$\nu=\lambda f$$ and E = hf then $$\lambda = \frac{h c}{E}$$

 

[rohanprabhu]

By size i meant: if 'h' could ever be equated to a wavelength, and h/2pi a radius of an electromagnetic wave.

I think you might be confusing the Planck's constant with Planck units.. http://en.wikipedia.org/wiki/Planck_units

 

[nuby]

I was also curious if the radius of a nucleon/particle could be determined by: h/p*2pi

And if wavelength and energy are ever considered to be the same.

for example, If the compton wavelength of a proton 1.32e-15 .. is applied to $$\lambda = \frac{h c}{E}$$
Could the result be the wavelength/energy of a particular atom?

Is there such a thing as a Planck radius?

 

[rohanprabhu]

I was also curious if the radius of a nucleon/particle could be determined by: h/p*2pi

A nucleon is a point particle and not an extended particle. What it means is that it doesn't have an associated radius as such.

And if wavelength and energy are ever considered to be the same.\

no. no two quantities are ever considered to be 'the same'. However, Energy is inversely proportional to wavelength for a wave with constant velocity.

for example, If the compton wavelength of a proton 1.32e-15 .. is applied to $$\lambda = \frac{h c}{E}$$
Could the result be the wavelength/energy of a particular atom?

In this equation, 'E' is the only unknown value. The energy 'E' is the energy required to determine the position of a proton within the length of the given wavelength. However, it is impossible to determine the position of a particle within it's Compton wavelength as the energy required to do so is enough to create a similar particle, which makes us impossible to determine the original particle's position.

Is there such a thing as a Planck radius?

Radius is basically a measure of length and is called 'radius' only when we speak in a specific context. And no, there is nothing like Planck radius.

 

[nuby]

In this equation, 'E' is the only unknown value. The energy 'E' is the energy required to determine the position of a proton within the length of the given wavelength. However, it is impossible to determine the position of a particle within it's Compton wavelength as the energy required to do so is enough to create a similar particle, which makes us impossible to determine the original particle's position.

I was thinking a more relativistic E there, and everything as a wave. (?)

$$\lambda = \frac{h c}{1.505e-10} = 1.32e-15$$

$$E = \frac{h c}{1.3214e-15} = 1.505e-10$$

 

[nuby]

Can you explain this to me? (from above)
In this equation, 'E' is the only unknown value. The energy 'E' is the energy required to determine the position of a proton within the length of the given wavelength. However, it is impossible to determine the position of a particle within it's Compton wavelength as the energy required to do so is enough to create a similar particle, which makes us impossible to determine the original particle's position.
Thanks in advance.

 

[rohanprabhu]

@nuby: if you are to determine any information regarding any system, you need energy to do so. When it comes to determining information about particles, collision of the particles with photons of a certain wavelength is used. Every measure you make has an associated uncertainty: the more accurate measure you make, the more energy you need. Say, you have to measure the position of an electron with a maximum uncertainty of 1 nanometer, you need photons of wavelength less than 1 nanometer. Every particle has a certain amount of energy, so does the electron whose position you want to measure. As your want a more accurate measurement, you need photons of higher and higher energy i.e of smaller and smaller wavelength. A point is reached when the energy of the photon becomes equal to that of the electron. At this point, when the energy carrying photon collides with the electron, there is enough energy to create another electron and hence it becomes impossible to determine the position of the electron as you are not even certain which electron was yours. The wavelength of this photon, which is just enough to create another similar particle, is known as the compton wavelength. This is the minimum uncertainty you will have when measuring the location of that particle. You can't get more accurate than that.

 

[malawi_glenn]

The Nucleon is NOT a point particle!

 

[nuby]

Thanks, rohanprabhu