Help Please?

Question

I solved part I and II, but I can’t solve part III. Help me please (thank you).

I)Find the wavelength of the photon emitted when a hydrogen from state n=4 to n=1
Ans: 9.7*10^-8 m

II)What is the momentum of this photon?
Ans: 6.6*10^-27 N.S

III) What is the recoil speed of the hydrogen atom after it has emitted this photon?

Answer 1

The way to solve this problem requires the mass of the hydrogen atom. Momentum = velocity times mass
Velocity therefore is momentum divided by mass.
Since a mole of hydrogen has the mass of 1 gram if you know how many atoms are in a mole the answer becomes easy. I don't remember for sure but believe that a mole contains 6.02*10^26 atoms. Look it up somewhere.
6.6*10^-27/(1/6.02*10^26)=6.6*10^-27*6.02*10^26
=3.96Meters per Second
check on what the molar constant value really is.

Answer 2

You did the hard parts. Use the conservation of momentum. Since you know the momentum of the photon. The hydrogen atom will have the same momentum = mass*velocity. So use the mass of the hydrogen atom and the momentum you already calculated to figure the velocity.