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 = 10⁹ eV)

Total energy of two y-rays: E = 10. 2 BeV = 10.2 x 10⁹ eV = 10.2 x 10⁹ x 1.6 x 10⁻¹⁹ J

Hence, the energy of each γ-ray:

E’ = E/2 = (10.2 x 10⁻¹⁰)/2 = 8.16 x 10⁻¹⁰ J

Planck’s constant, h = 6.626 x 10 ⁻³⁴ Js

Speed of light, c = 3 x 10⁸ m/s

Energy is related to wavelength as:

E’ = hc/λ

Therefore , λ = hc/E’

= (6.626 x 10⁻³⁴ x 3 x 10⁸)/( 8.16 x 10⁻¹⁰)

= 2.436 x 10^-16 m

Therefore, the wavelength associated with each γ-ray is 2.436 x 10^-16 m.