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In an accelerator experiment on high ene...

In an accelerator experiment on high energy collisions of electrons with positron, a certain event is interprected as annihilation of an electron-positron pair of total energy 10.2 BeV into two `gamma`-rays of equal energy. What is the wavelength associated with each `gamma`-ray ?
`(1 BeV=10^(9)eV)`

Text Solution

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Energy of electron - positron pair `=10.2 BeV=10.2 xx 10^(9)eV`
`therefore` Energy of one `gamma`-ray photon
`E=(10.2xx10^(9))/(2)eV=5.1xx10^(9)xx1.6xx10^(-19)J=5.1xx1.6xx10^(-10)J`
But `E=h upsilon="h"(c )/(lambda)`
`lambda=(hc)/(E )=(6.63xx10^(-34)xx3xx10^(8))/(5.1xx1.6xx10^(-10))=2.44 xx 10^(-14)m`
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