Question

An electron with a speed of 1.3 ×106m/s collides with an atom of element X. Shortly afterward, the atom emits a 1240 nm photon. What was the electron's speed after the collision? Assume that, because the atom is so much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.

Answer 1

Initial energy of the electron E = ( 1/ 2) m v 2
where m = mass of electron = 9.1 * 10^-31kg
           v = speed = 1.3×10^6 m/s
So, E = 7.6895 * 10^-19 J
wavelength of the photon λ = 1240 nm
                                          = 1240 * 10^-9 m
energy of the photon E ' = hc / λ
where h = planck's constant = 6.625 * 10^-34 Js
           c= speed of light = 3 * 10 8 m / s
substitue we get E ' = 1.6 * 10 -19 J
∴energy of the electron after collision E " = E -E '
                                                               = 7.6895 * 10 -19 - 1.6*10^-19
                                                               = 6.0895*10^-19 J
So, speed of the electron after collision v = √[2E " / m ]
                                                               =1.156 * 10^6 m / s