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Compton Effect and the E-Bomb

The Compton Effect: The wavelength of electromagnetic radiation increases after colliding with electrons.

The Compton Effect occurs when a high energy gamma-ray (or other form of electromagnetic radiation) photon collides with an electron. The photon gamma-ray and the electron are deflected at an angle, and because the photon loses energy and momentum to the electron, so the photon comes out of the collision with a longer wavelength. The longer the wavelength, the bigger the angle. Compton scattering is what we call the deflections and the change of wavelength. The Compton effect usually occurs with high energy gamma-rays and low atomic numbers because their electrons are more loosely bound to the nucleus.

We can use a formula to determine either the incident wavelength, the scattered wavelength or the angle of deflection.

WL2 - WL1 = (h/(mec))(1-cos)
WL
is wavelength measured in meters.
h is Planck's constant equal to 6.625x10-34 J-S
me is the mass of an electron equal to 9x10-31 kg
c is the speed of light equal to 3x108 m/s
cos is the cosine of the angle of deflection.

The e-bomb is also known as an electromagnetic pulse (EMP) weapon. You may have heard of it in the news or in the movie The Matrix (near they end, they use it to kill the sentinels that were attacking the Nebuchadnezzar).

The e-bomb takes advantage of the dependency people have on electricity. It spares lives and buildings, but once it's detonated it has the potential to destroy machines that use electricity.

Electric current produces magnetic fields and changing magnetic fields induce electric current. The idea behind the e-bomb is to create a magnetic field that is too much for the electrical circuitry.

When an e-bomb goes off (here's where Compton's effect comes in) the gamma radiation photons from the bomb deflect a lot of electrons from the atmosphere's nitrogen and oxygen atoms. The freed electrons interfere with the Earth's magnetic field and produce a fluctuating electrical current. The current then induces a potent magnetic field. The electromagnetic pulse induces an overwhelming electrical current in conductive materials ultimately destroying them and any electrical devices feeding off them.

Problem: Trinity detonates an EMP weapon to destroy some robots. The bomb releases gamma rays with a wavelength of 3x10-11 m and the deflect with nitrogen and oxygen electrons at an angle of 45 degrees. What is the wavelength of the scattered gamma-rays?

WL2 - WL1 = (h/(mec))(1-cos45)
WL2 - 3x10-11 = (6.625x10-34/((9x10-31)(3x108)))(1-cos45)
WL2 - 3x10-11 = 7.19x10-13
WL2 = 3.07x10-11 a slight difference, but a longer wavelength nonetheless!

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