(In each case, because we have switched to photons, the energy on the left has to be increased by a factor of 2).

1.

dp.dx. >= h/(4Pi)

dh/lambda  . dx  >= h/(4Pi)  (substituting for the momentum of a photon)

dh.nu/c . dx >= h/(4Pi)  (rewriting the wavelength in terms of frequency and light speed)

dE/c . dx >= h/(4Pi)

dE.dx >= hc/(4Pi) (multiplying through by the speed of light) 

2.

Using two different variables which define the Uncertainty Principle

dE.dt    >=    h/(4Pi)

Now, since speed = distance/time; therefore time = distance/speed. Then, for a photon the speed is the speed of light c and the change in distance = dx.

Therefore dE.dx/c >= h/(4Pi)    So    dE.dx    >=    hc/(4Pi)

3.

dp.dx    >=    h/(4Pi)

d(mv).dx    >=    h/(4Pi) (Since momentum p = mass m x velocity v)

For a photon, the velocity v is the speed of light c and m is the equivalent mass using Einstein's mass energy relation, E/c^2.

Substituting these in the above we are lead to the same result:

dE.dx    >=    hc/(4Pi)

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