In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as 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 = 10⁹eV)

Solution

Total energy of 2 γ-rays = 10.2 BeV = 10.2 x 10⁹ eV

∴ Energy of each γ-ray is,

E = \frac{1}{2} (10.2 \times 10^{9} \times 1.6 \times 10^{- 19}) J

= 8.16 \times 10^{- 10} J

Now, using the formula for energy of a photon,

E = hv = \frac{hc}{λ}

\Rightarrow

λ = \frac{hc}{E} = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{8.16 \times 10^{- 10}} = 2.436 \times 10^{- 16} m .

is the required wavelength assosciated with each γ-ray.

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