Ejercicio Problem 9. Electron Orbital Transition and Deflec… · Física I URV Setembre

Problem 9. Electron Orbital Transition and Deflection Angle

In the pre-quantum Bohr model of the hydrogen atom, an electron of mass $m$ initially describes a stable circular orbit with radius $r_0 = 5a_0$ and tangential speed $v_0$ around the nucleus.

Due to bombardment by radiation, the electron undergoes an instantaneous change in its direction of motion without any change in its speed. As a result, it transitions into an elliptical orbit whose distance of closest approach to the nucleus (periapsis) is $r_p = a_0$.

a)

Determine the speed of the electron at the periapsis ($v_p$) of the newly formed elliptical orbit in terms of $v_0$.

$v_0$

b)

Find the deflection angle $\theta = \beta$ (or deviation $\beta$ relative to the original velocity vector) by which the trajectory was rotated at the impact point. Express the angle in degrees.

°