Calculating Recoil Energy and Velocity for Hydrogen Atom Transition [SOLVED]

[cks]

[SOLVED] recoil energy

Homework Statement

Calculate the recoil energy and velocity of a hydrogen atom in a transition from
the state « = 4 to the state AT = 1, in which a photon is emitted.

Homework Equations

E=-13.5/n^2

E=mc^2/sqrt(1-v^2/c^2)

The Attempt at a Solution

|E4-E1|=13.6-13.6/16 eV = 12.75 eV

Invoking the total energy,

Before emission
mc^2 = E recoil + |E4-E1|=> E recoil = 1.50 *10^-10 J

I couldn't get the correct answer. I wonder what is wrong? am I understanding the meaning of recoil energy wrongly?

 

[Shooting Star]

Recoil energy only pertains to the KE, and should not include the rest energy.

 

[cks]

Thank you, I finally got it.

 

[cks]

$${\frac {-1/4\,i}{w}}$$