Photons

I was reading a SciFi book which had some particle suddenly becoming a photon and taking off at the speed of light.
So I wake up this morning and, lying in bed, think about the consequences of that event.
That suggested the question: What's the wavelength of the photon? Would the "light" be visible?
So I figure I might be able to calculate the frequency of that photon:

>You're kidding, right?
Gimme a chance, eh?

The momentum of a particle is (usually) given by:
[1]   p = mv
where m is the particle mass and v its velocity.

Further, according to Einstein's Theory of Relativity:
[2]   E = mo c2 / [ 1 - v2 / c2 ] 1/2
where E is the Energy of the particle, c is the velocity of light and mo is the particle mass when it's at rest.

If you juggle [1] and [2], you can generate:
[3]   E2 = moc4 + p2c2
where p = m v and m = mov / [ 1 - v2 / c2 ] 1/2.

Okay, so we stick mo = 0 in [3] and get an Energy which we can associate with a massless particle like the photon, namely:
[4]   E = pc

Okay, so if there's Conservation of Momentum, when a particle with mass m and velocity v turns into a photon, the massless photon momentum would be determined as:
[5]   p = mv = E/c
using [3] with mo = 0 and mv is to the momentum of the particle (before it turned into a photon).

That is, the photon would have Energy determined by the particle's momentum via:
[6]   E = (mv)c

Aah, but there's a relationship between the Energy of a light-photon and its frequency, namely:
[7]   E = h f
where f is the frequency of the light and h is Planck's constant: h = 6.626 x 10-34 Joule-seconds.

Note: In [7], you multiply Joule-seconds by f (measured in 1/seconds) and you get Energy ... measured in Joules.

So where are we?
The particle that turned into a photon has a frequency associated with it, namely:
[8]   f = (mv)c / h   Hertz
where (as before) mv is to the momentum of the particle before it turned into a photon.

Suppose we consider an electron turning into a photon. Suppose, further, that it's travelling at 1% of the speed of light. We'd have:
mo = 9.1 * 10-31 kg and v = c/100 which would give (via [8]):
[9]   f = (9.1 * 10-31) (c/100) / 6.626 x 10-34 = 1.2 x 1016 Hz or 12,000,000 GigaHertz or 12,000 TeraHertz or 12 PitaHertz (ultraviolet radiation)
... using c = 3 x 108 m/s.

The wavelength of that radiation would be in the range of molecular sizes:

 The human eye can see up to 340 TeraHertz. I guess we couldn't see it, eh? >zzzZZZ

Note:
Are photons really without mass?
Since Einstein's magic equation, E = m c2, generates an equivalence between Energy and mass, presumably we can associate a mass with a photon.

>zzz - huh?
A photon has Energy (according to [7]) so it has an "associated" mass, namely h f / c2.
But, tho' it's sometimes called the "relativistic mass", can we weigh it on a bathroom scale?
Is it anything like ordinary, garden variety masses (like that of an electron)?

Apparently the debate continues as to whether a photon has "real" mass.
Of course, since a photon moves with the speed of light, it don't make much sense to talk of its "rest mass".