Question

To remind you, in Physics 101 you learned that the momentum ~p of an object with mass m traveling with velocity ~v is given by ~p = m~v. The magnitude of the momentum of a photon has been found to be given by |~pphoton| = h/λ, where h is Planck’s constant and λ is the photon’s wavelength. The direction of the photon’s momentum is the direction in which the photon is moving. Suppose that a hydrogen atom that is initially at rest and in its n = 6 level makes a transition to its n = 1 level, emitting a photon in the process.

(a) What is the energy (in Joules) of the emitted photon?

(b) What is the wavelength (in meters) of the emitted photon?

(c) Assuming that the total momentum of the system is conserved, what is the speed with which the hydrogen atom is traveling after the photon has been emitted?

Answer 1

Energy (E = E-E, E.- Energy of è in n=6 state E = -13.6 - / - 13-6) er (612 " En = -13.6er nz E = 13.22 er (b) - 21.15 were length (d) = 10-19 J hc wore ter 6.64 x 10-34 X 3x108 13-22 x 106 x 10-19 • lev= 1.6x10-19 30.942 x 10-7 m) Conservation of momentum - oa MAVH - E momentum of - VH= photon E CMH - e mu- mass of hydrogen atom - 21. 158 16-19 Sweet 3x108 x 1067x10-27 Selfie/ Vee 4.22 me