KE =Quantum energy-Threshold energy
$\Rightarrow \large\frac{6.626\times 10^{-34}\times 3\times 10^8}{3000\times 10^{-10}}-\frac{6.626\times 10^{-34}\times 3\times 10^8}{4000\times 10^{-10}}$
$\Rightarrow 6.626\times 10^{-19}-4.9695\times 10^{-19}$
$\Rightarrow 1.6565\times 10^{-19}$J
$\large\frac{1}{2}$$mv^2=1.6565\times 10^{-19}$
$m^2v^2=2\times 1.6565\times 10^{-19}\times 9.1\times 10^{-31}$
$mv=5.49\times 10^{-25}$
$\lambda=\large\frac{h}{mv}$
$\Rightarrow \large\frac{6.626\times 10^{-34}}{5.49\times 10^{-25}}$
$\Rightarrow 1.2\times 10^{-9}m$
Hence (b) is the correct answer.