①  As the power is 10 kW and the light is on for 5 seconds, the energy delivered to Cormorant by the laser burst will be:

Energy = power x time   =  10 000 x 5  =  50 000 J.

Now the energy of each individual photon is given by E = hν  =  hc/λ. So for Nefertiti’s laser:

E = 6.63 x 10-34  x  3.00 x 108 / 10.6 x 10-6   =   1.88 x 10-20 J

Therefore the number of photons delivered to Cormorant will be:

50 000 / 1.88 x 10-20  =  2.66 x 1024 photons.  

②  The momentum carried by each photon, p = h / λ  =  6.63 x 10-34 / 10.6 x 10-6  =  6.25 x 10-29 kgms-1.

So the total momentum carried by all those photons

= 2.66 x 1024 x  6.25 x 10-29  =  1.66 x 10-4 kgms-1.

Assuming all the photons are reflected directly backwards when they hit Cormorant, the momentum transferred to him will be twice this value, in order for total momentum to be conserved:

Total momentum gained by Cormorant =  2 x 1.66 x 10-4  =  3.32 x 10-4  kgms-1

③   So (using the classical formula for momentum, as we are not going to be dealing with velocities near light speed here), the increase in Cormorant’s velocity will be:

Δv  =  Δp / m   =  3.32 x 10-4 / 2.5  =  1.33 x 10-4 ms-1.

So Cormorant can only expect to gain around one tenth of a millimetre per second from this irradiation. He’s probably not going to notice.