Calculate Speed of Recoiling Hydrogen Atom After Transition to Ground State

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A hydrogen atom transitioning from the n = 4 state to the ground state emits a photon, leading to recoil. The energy difference calculated is 12.75 eV, and the mass to consider is that of a hydrogen atom, approximately equal to the mass of a proton. Conservation of momentum is crucial in this scenario, as the recoil speed can be determined using the emitted photon's energy. The problem can be solved without additional information by applying the principles of conservation of momentum and energy. Understanding these concepts is essential for calculating the speed of the recoiling hydrogen atom.
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A hydrogen atom, initially at rest in the n = 4 quantum state, undergoes a transition to the ground state, emitting a photon in the process. What is the speed (in terms of m/s) of the recoiling hydrogen atom?

anyone knows what to do? i calculated the energy difference and got 12.75 eV and i calculated the potential energy as well, but i don't know which mass to assign the atom...

any help is appreciated...
 
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(1) What's conserved during the emission?
(2) You can look up the mass of a hydrogen atom!
 
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well, that's the thing- the problem doesn't state anything more than I put on there... the mass of a hydrogen atom will be that of 1 proton, but I'm not sure if that's what i should look for...

any thoughts?
 
You don't need any more information to solve the problem. What's the answer to my first question? (Hint: In any kind of "explosion", what's conserved?)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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