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A positron and an electron collide and a...

A positron and an electron collide and annihilated to emit two gamma photons of same energy. Calculate the wavelengths corresponding to this gamma emission.

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`._(+1)e^(0) + ._(-1)e^(0) rarr 2 gamma` (photons of same energy)
The mass of two electrons is converted into energy.
The energy produced emission of two photons
`= 2 xx m_(e) xx c^(2)`
`= 2 xx 9.108 xx 10^(-31) xx (3.0 xx 10^(8))^(2) = 163 xx 10^(-15) J` ltbgt Energy produced per photon
` = (16.39 xx 10^(-14)J)/(2) = 8.195 xx 10^(-14) J`
Using Eistein equation,
`E = (hc)/(lambda)`, where `c =` velocity of ligth, `lambda =` wavelength of particle
`:. 8.195 xx 10^(-4) = (6.625 xx 10^(-34) xx 3.0 xx 10^(8))/(lambda)`
`:. lambda = (6.625 xx 10^(-34) xx 3.0 xx 10^(8))/(8.195 xx 10^(-14)) = 2.425 xx 10^(-12) m`
`lambda = 2.425 pm`
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