Question

A stationary He+ ion emitted a photon corresponding to a first line of the Lyman series. The photon liberated an electron from a stationary H atom in the ground state. What is the velocity of the electron?

(a) 2.18 x 10^6 m/s
(b) 4.36 x 10^6 m/s
(c) 5.44 x 10^6 m/s
(d) 1.09 x 10^7 m/s

Answer 1

To calculate the velocity of the electron, we can use the conservation of momentum and the energy of the photon. By equating the momentum and solving for the velocity of the electron, we can find that the velocity is approximately 2.18 x 10^6 m/s (option a).

Step-by-step explanation:

To calculate the velocity of the electron, we can use the conservation of momentum. Since the He+ ion is stationary, the momentum before and after the interaction must be equal. The momentum can be calculated using the mass and velocity of the electron.

The energy of the photon can be found using its wavelength and the equation E = hc/λ, where h is Planck's constant and c is the speed of light. This energy is equal to the ionization energy of the hydrogen atom, which can be calculated using equation E = -13.6eV.

By equating the momentum and solving for the velocity of the electron, we can find that the velocity is approximately 2.18 x 10^6 m/s (option a).