# Energy required to reach 1 wavelength [closed]

I was curious if there was a forumla to find the energy required to reach 1 wavelength in a given substance. (or a vacumn if that's too hard).

I am also wondering if this number can tell us anything about the way the wave acts?

My knowledge of electromagnetic radiation is pretty small... Maybe these things don't really matter?

• " reach 1 wavelength in a given substance" doesn't really mean anything - what are you trying to say? – Martin Beckett Feb 1 '12 at 23:11
• How much energy does it take 1 wavelength does it take 144mhz radiation go one wavelength (6 feet) vs how much energy does it take 800hz radiation go one wavelength (250 miles). Since there is such a difference to reach different wavelengths... Wouldn't it take differenet amounts of energy to do so? – Kyle Hotchkiss Feb 1 '12 at 23:19
• Energy is force over distance. You have the distance part (1 wavelength), but what force are you thinking about providing the energy (or absorbing it) ? – John Alexiou Feb 3 '12 at 19:45

The energy of a photon depends only on its frequency, or equivalently its wavelength: $$E=h\nu=\frac{hc}{\lambda}$$

So the energy of a $144MHz$ photon is ~$6\times10^{-7}eV$; and the energy of a $800Hz$ photon is ~$3.3\times10^{-12}eV$. (I assume you mean MHz megahertz, and not mHz millihertz)

It doesn't matter how 'far' they travel, since distance is irrelevant from the viewpoint of a photon that travels at the speed of light.

Edits must be at least 6 characters...

• Interesting. I don't have any formal education in physics and i guess I may have been applying mechanical wave properties this way. – Kyle Hotchkiss Feb 2 '12 at 0:10
• So the initial energy doesn't impact distance... But a certain amount of initial energy is needed to reach a certain frequency? – Kyle Hotchkiss Feb 2 '12 at 0:13
• As @Martin alludes to above, it's not correct to think of photons as "using" or "needing" energy to travel. They always travel; that's what they do, and always at the speed of light. A photon doesn't need to "reach" a frequency: when it is emitted, it already has that frequency. It's not like a mechanical wave. Photons essentially are energy. And absent hitting something, a photon will keep travelling to infinity. – Mark Beadles Feb 2 '12 at 0:21
• Thanks, @Community♦ for catching my error in the sign of the exponent. – Mark Beadles Feb 2 '12 at 15:52

It doesn't take any energy for a photon of a given wavelength to travel any distance. Assuming you are in empty space a photon will travel essentially forever - the cosmic microwave background is photons that have been travelling to us for nearly 15Bn years.

Travelling in a medium light will lose some energy to the stuff it's travelling through, how strongly will depend on both the medium and the wavelength. Since light loses energy by interacting with the stuff the absorption is generally stronger for shorter wavelengths (higher energies) so X-rays and UV are absorbed very strongly in a short distance while infrared and radio go further through.

You also need to differentiate between a beam of light losing power as individual photons are absorbed, and a photon losing energy as it is absorbed and remitted at a longer wavelength (lower energy)