1g object absorbing 632nm photons to reach 1mm/s

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Homework Statement


I have a 1g object on a frictionless surface being hit with light of a frequency 632nm (directly parrallel to the surface and the object absorbs all the light). How many photons did the object absorb by the time it's moving at 1mm/s?


Homework Equations




The Attempt at a Solution


Well I worked it out two different ways and I got two different answers:

My first attempt is via conservation of energy:
n*h*c/lambda + m*c^2 = gamma*m*c^2
where
n is the number of photons
h is Planck's constant
c is the speed of light
lambda is the wavelength
m is the mass of the object
gamma is the 1/sqrt(1-v^2/c^2)
Then I solved for n.

My second attempt is via conservation of momentum:
n*h/lambda = gamma*m*v
Then I solved for n.

In both cases I got different answers. So I'm not sure what's wrong.
 
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Discussion

Trust conservation of momentum before you trust a naive conservation of energy calc. The collision is inelastic.
 
Ok thanks. But what happened to the energy? Did it radiate as heat or something?
 
Some of it could have been converted into electrical energy if the surface is connected to a power grid. Conservation can't tell you where it went. But yes, most likely answer is heat.