In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as the annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy. What is the wavelength associated with each γ-ray? (1BeV = 109 eV)
Given:
Total energy of system, E = 10.2 BeV = 10.2 × 109 × 1.6 × 10-19J
E = 16.32 × 10-10J
Energy in each ray, E’ = E/2
E’ = 8.16 × 10-10J
We know that Energy in a photon is given by,
…(1)
Where,
E = Energy of photon
h = Planck’s constant = 6.6 × 10-34 Js
c = 3 × 108 ms-1
λ = wavelength of photon
From equation (1) we can get,
λ = 2.34 × 10-16m
Hence, the wavelength of each ray is 2.3 × 10-16 m.
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