How to solve this questions in detailed solution? If a proton and an anti-proton

Question

How to solve this questions in detailed solution?

If a proton and an anti-proton annihilated each other, what frequency of light would be emitted? Compare this with frequency produced by the annihilation of an electron-positron pair discussed in class. Where on the electromagnetic spectrum do these energies belong? The rest energy of the electron is 511 KeV. What is the rest energy of the proton? Do a little research and compare these energies with the particle energies energy attained by the Large Hadron Collider.

Explanation / Answer

We know that,

Mp = 1.67 x 10-27 kg ; c = 3 x 108 m/s

Energy of a photon = E = mc2 =  1.67 x 10-27 x ( 3 x 108)2 = 15.03 x 10-11 J

We know that, E = h f where h is the plank's constant and f is the frequency.

Energy emitted will actually be two times of energy we have calculated, because even the antiproton has got the same energy. So

f = 2E / h = 2 x 15.03 x 10-11 J / 6.6 x 10-34 m2 kg / s = 4.6 x 1023 Hz

Hence, the frequnecy of light emitted will be = f = 4.6 x 1023 Hz. It belongs to Gamma rays in electromagnetic spectrum.

The rest energy of proton has already been calculated:

E = mc2 =  1.67 x 10-27 x ( 3 x 108)2 = 15.03 x 10-11 J = 9.36 x 108 eV = 9.36 x 105 keV

Hence, the rest energy of proton =  9.36 x 105 keV.

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