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 $10.2 \times 10^{9}$eV into two of equal energy. The wavelength associated with each $\gamma - ray$is:

• A. $3.21 \times 10^{- 18}m$
• B. $1.23 \times 10^{- 16}m$
• C. $2.44 \times 10^{- 16}m$
• D. $4.21 \times 10^{- 14}m$

Answer 1

Answer: (C)

$2.44 \times 10^{- 16}m$

Answer 2

: Here total energy of $2\gamma - rays = 10.2 \times 10^{9}eV$

$\therefore$Energy of each $\gamma - rays$

}{= 8.16 \times 10^{- 10}j}$$ As $E = h\upsilon = \frac{hc}{\lambda}$ Or $\lambda = \frac{hc}{E} = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{8.16 \times 10^{- 10}} = 2.44 \times 10^{- 16}m$