LASER Operating At A Certain Frequency

[Paradox101]

Q. A LASER is operating at a frequency f = 6.1*10^14 Hz.
A)Calculate the momentum of the photon emitted by the laser.
B)A helium atom flies towards the laser at a speed of v = 3.5 m/s.During one laser pulse the gold atom absorbs on average 5 photons.Find the speed the helium atom after one laser pulse.Treat the interaction between photons and the helium atom as an inelastic collision.Use m=4.0u for mass of the helium atom.

ATTEMPT: wavelength λ= c/f = 3×10^8/6.1×10^14
≈492 nm.
⇒Total momenta of 5 photons in 1 pulse =5×h/λ =5×6.63×10^-34/4.92×10^-7
= 5×1.35×10^-27
= 6.75×10^-27 kg.m/s
Again, like in the previous question i posted, i can't figure out how to find the speed of the helium atom.
(Here i can't divide the momenta of 5 photons by the mass of the He atom)
BTW the mass of the He atom will probably be :-
M(He)=4×1.6605×10^-27
= 6.64×10^-27 kg
That's as far i can get.I guess what i must do is deal with the conservation of linear momentum but i am not sure.Any suggestions?I really must complete these questions in time.

 

[BvU]

It's all you've got and it holds. No big deal!

 

[Paradox101]

But the one who gave these questions isn't going to hold! Haven't you got a soluti-----I mean hint?

 

[BvU]

Treat it as a fully ineastic collision: add up the momentum of the photons and the He, to get the momentum after the absorption. Then divide by the He mass to get its velocity.

 

[Paradox101]

You mean p_photons/M_He=6.75×10^-27/6.64×10^-27=1.01 m/s.But the answer is 2.5 m/s

 

[Paradox101]

Found it! it should be done like this:
p_He before collision=Mu=6.64×10^-27 × 3.5
= 2.324×10^-26 kg.m/s

So,apparently, Mv=p_He-p_photons
=6.75×10^-27-2.324×10^-26
=1.65×10^-26kg.m/s
and v = Mv/M=1.65×10^-26/6.64×10^-27
= 2.5 m/s
YAY

 

[BvU]

Well done.