start with Einstein's famous equation which relates energy
'E' of an object to its mass 'm' and the speed of light
E = m c2 =
m c c.
de Broglie realised that 'm c' was simply
the photon momentum, p (mass x velocity). So, we can now
E = p c.
The speed of light 'c' can also be expressed
c = f ,
where 'f' is the frequency of the light
and is its wavelength.
Remember that we also know from Planck's
E = h f.
Putting all this together we have
h f = p f .
h / p = ,
i.e.: as the wavelength of light decreases,
the momentum of the photons increases.