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

Ans : (d)

Energy of each $\gamma-ray,E’ = \large\frac{total\: energy}{2}$

$= \large\frac{10.2 \times 10^9 \times 1.6 \times 10^{-10} J}{2} = 8.16 \times 10^{-10} J$

$E’=\large\frac{hc}{ \lambda}$

$\Rightarrow \lambda = \large\frac{hc}{E’}$

$= \large\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{(8.16 \times 10^{-10} )} = 2.436 \times 10^{-16}m$

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