Given: Mass of the block $m=100 \mathrm{g}$, initial velocity of the block $u=2 \mathrm{m} {\mathrm{s}}^{-1}$, and final velocity of the block $v=\frac{u}{2}=1 \mathrm{m} {\mathrm{s}}^{-1}$.

As non-conservative forces are not acting on the system we can conserve energy.

Thus, loss in kinetic energy of block $=$ Gain in potential energy of spring

$T.E{ }_i=T.E{ }_f$

$\frac{1}{2}m{u}^2=\frac{1}{2}m{v}^2+\frac{1}{2}k{x}^2$

$\frac{1}{2}\times 0.1\times 2^2=\frac{1}{2}\times 0.1\times 1^2+\frac{1}{2}k\times 0.{02}^2$

$k=750 \mathrm{N} {\mathrm{m}}^{-1}$