Answer
If we double the kinetic energy, the de Broglie wavelength decreases by a factor of $\sqrt{\frac{1}{2}}$
Work Step by Step
We can use Equation (38-20) to find an expression for the de Broglie wavelength:
$K = \frac{h^2}{2m \lambda^2}$
$\lambda^2 = \frac{h^2}{2m~K}$
$\lambda = \sqrt{\frac{h^2}{2m~K}}$
If we double the kinetic energy, the de Broglie wavelength decreases by a factor of $\sqrt{\frac{1}{2}}$
