Understanding the Relationship between Planck's Constant and Frequency

[petr1]

Could you please explain me, what's the relationship between Planck's constant and frequency. Why does higher frequency mean higher energy? Maybe I'll need some explaining on Planck's constant too.

Someone explained me that h is an energy of a 'packet' and you could think frequency as amount of those packets in a photon. But this creates the problem that frequency could be only an integer because you couldn't divide h into smaller energy packets.

 

[Simon Bridge]

Welcome to PF;
You do need to read up on Plank's constant - it is the ratio of the energy of a wave to it's frequency in the model that energy can only come in discrete lumps. The value of h is something you measure experimentally.

So - on the face of it, asking why h=energy/frequency for light is a bit like asking why pi=circumference/radius for a circle.

But you should be able to see why higher frequencies must mean higher energy just by experience - wave your arms vigorously. You get tired don't you. If you wave your arms just as high but you do it faster (same amplitude, higher frequency) you get tired faster. Thus it should come as no surprise that waves that oscillate at higher frequencies have more energy.

 

[tia89]

Someone explained me that h is an energy of a 'packet' and you could think frequency as amount of those packets in a photon. But this creates the problem that frequency could be only an integer because you couldn't divide h into smaller energy packets.

Probably it would be better to call it a "quantum" instead of a "packet", as they have different meanings in physics.

The point is that actually the frequency $\nu$ is continuous. It is light which comes quantized in an integer number of these quanta, instead than as a continuous flux of energy.

Therefore what you have is that if you take a monochromatic (assume perfect monochromaticity for simplicity, like a laser for example, meaning that you have light with only ONE frequency) beam of light, each photon (i.e. quantum of light) of the beam has an energy given by $h\nu$, and the beam has an energy which is the sum of the energies of all photons, and therefore it is given by $Nh\nu$ where $N$ is the number of photons in the beam.

The point is that in everyday life a beam of light has a really large number of photons, and the energy of a single photon is so small, that we cannot perceive this quantized nature and we see light as continuous; indeed the difference of energy when we have one or two photons more or less is so small that it can't be perceived as discrete.

 

[Simon Bridge]

Good point - I failed to stress that the size of the discrete lumps of energy depends on the frequency - which can be continuous. Thanks.