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# 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 $\gamma$-rays of equal energy. What is the wavelength associated with each $\gamma$-ray? $(1\; Bev = 10^9\: eV)$

$\begin {array} {1 1} (a)\;2.436 \times 10^{-18} m & \quad (b)\;2.436 \times 10^{-17} m \\ (c)\;243.6 \times 10^{-17} m & \quad (d)\;2.436 \times 10^{-16} m \end {array}$

Ans : (d)
Energy of each $\gamma-ray,E’ = \large\frac{total\: energy}{2}$
$= \large\frac{10.2 \times 10^9 \times 1.6 \times 10^{-10} J}{2} = 8.16 \times 10^{-10} J$
$E’=\large\frac{hc}{ \lambda}$
$\Rightarrow \lambda = \large\frac{hc}{E’}$
$= \large\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{(8.16 \times 10^{-10} )} = 2.436 \times 10^{-16}m$

edited Mar 13, 2014