[RFC][Info] Playing with Boom-Boom (Or, Antimatter and You - A Children's Parable)

[Black Aeronaut]

Okay, so earlier I was thinking about how much physical recoil these beam-shots would have, because, facts are facts, photons have mass.

So let's go with the two examples I gave for in-setting use:

However, what Jail doesn't know about is that Washu and Ben had been working on perfecting Ben's secondary mode: the Beam Cannon - where he annihilates a M/AM mix in his 'gun barrel', collimates the particles and photons, and unleashes hell.

And HELL indeed!!!  Joules translate directly into Watt/Seconds, or just Watts.  Running Labster's math, adjusted to fit with annihilation of ten nanograms of antimatter with ten nanograms of matter:

10^-8 kg * 2 * 8.988×10^16 m^2/s^2 = 1,797.6 MJ ... or about 1.8 GIGAWATTS.

The first time he fires that bad boy off, it's gonna make for a light show that, even though it only lasts for a second, will attract ALL KINDS of attention!  That might even be strong enough to have actual recoil to it!

".... Uhm, yeah.  I think I'm gonna have to reduce the yield on that bad boy."

And then...

And boy, does Ben ever soften it up.  He waits until the ten-minute cool-down passes, and then fires up a Level 1 (1 μg) Beam Shot.

Math?  Math.

10^-6 Kg * 2 * 8.988*10^16 m^2/s^2 = 180 GIGAWATTS.

..... I'm not quite sure, but I suspect Ben just may have outdone Nanoha here.

And then tacky and crass jokes will abound about Ben feeling sore after that.  And not only Ben.  When Nanoha gets older and she and Fate start to... ahhh, experiment, Fate will derive no end of amusement by teasing Nanoha over it.

"You can't lie to me, Nanoha~.  I saw how flushed you were he did that~."

After that, Washu has a suggestion for Ben: Don't even think about firing off a Level 0 or greater in Beam Shot mode.  Masu-enhancement or not, she does not believe he can handle the strain.

So.

Momentum of an photon is given as p=h/λ, where p is the momentum of the photons (given as kg*m/s, which, quite conveniently translates directly into Newton-Seconds), h is the Planck Constant (Joule-Seconds), and λ is your photon's wavelength (Meters).

Wait.  We need to figure out what the wavelength is.

Fortunately, there's a formula for that, too.

λ = (hc)/E, where λ=wavelength in meters, h=Planck Constant in Joule-Seconds, c= Speed of Light in meters per second, and E is your energy in Joules.  NOW, I know that not everything is gonna be on this same wavelength... But I'm just gonna go Law of Averages, baby, and roll with it.

Math?

Math.

From the above quoted math we know that a 10ng Beam Shot, AKA Level 3, puts out around 1,797.6 MJ (1.7976*10^9)

So, wavelength...

((6.626*10^−34)*(3*10^8))/(1.7976*10^9)=
(1.9878 × 10^-25)/(1.7976*10^9)=
1.1058*10^-34 Meters  (Good grief!!!)


And now the impulse...

(6.626*10^−34)/(1.1058*10^-34)=
5.99 kg*m/s

Damn-near six whole fricken Newton-Seconds.

To give you an idea of what that's like, 1 N s is the same as a 420 gram football (FIFA specified weight for outdoor size 5) kicked to a speed of 8.6 km/h.
2.6 N s is the same as a 9x19 mm 7.5 gram pistol round launched at 350 m/s.
3.8 N s is the same as a 5.56 mm (0.223) 4 gram rifle round launched at 945 m/s.
And 6 N s is the same as the total impulse of a class C model rocket engine.

That's actually pretty damn substantial.

Now, what about the 180 GW "Level 1" shot?

Since you've already seen how the math is worked out, I'm gonna get cute here with Wolfram Alpha and plug the whole damn thing in at once.

p=h/((hc)/E)

(6.626*10^−34)/(((6.626*10^−34)*(3*10^8))/(1.7976 × 10^11))=
599.2 Kg*m/s

HOLY

FUCK

600 N s

!?!?

Just...  WOW.

For those of us that are Metric-impaired, that's about 135 lbs of Force.

Folks.

Benjamin is about to go like this:




Literally.  Like that.

Sources:
https://en.wikipedia.org/wiki/Newton_second#Examples
https://courses.lumenlearning.com/physic...-momentum/
https://www.youtube.com/watch?v=MsQ2GIefY58