Question

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? $(1BeV={10}^{9}eV)$

Answer 1

The total energy of the pair is:

$E=10.2BeV$

$\Rightarrow 10.2\times {10}^9\times 1.6\times {10}^{-19}J$

$=1.632\times {10}^{-9}$

Energy per $\gamma$-ray is $E_1=E/2$.

Now, $E_1=\frac{hc}{\lambda }$

$\Rightarrow \lambda =\frac{hc}{E/2}$

$\Rightarrow \frac{6.6\times {10}^{-34}\times 3\times {10}^8}{1.632\times {10}^{-9}/2}=2.436\times {10}^{-16}m$