If the momentum of the protons is doubled then the de Broglie wavelength of protons will reduce by a factor of 2.
The de Broglie equation is one of the equations that is widely used to define the wave properties of matter.
It basically illustrates how an electron acts as a wave.
Electromagnetic radiation's dual nature as a wave and a particle with motion (expressed in frequency, wavelength).
Microscopically small electron-like particles were used to demonstrate the existence of this dual nature feature.
The formula is provided by
λ = h/mv = h/p
where
Momentum (p) = mv
It is evident from the equation that the relationships between wavelength and momentum are inverse.
So if the momentum of the protons is doubled then the de Broglie wavelength of protons will reduce by a factor of 2.
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