The allowed energies of a simple atom are 0.0 ev, 5.5 ev and 9.0 ev. an electron traveling at a speed of 1.8*106 m/s collisionally excites the atom. part a what is the minimum speed the electron could have after the collision?

The possible transitions of the electrons are from 0.0 ev to 5.5 ev and from 5.5 ev to 9.0 ev.

The minimum change in energy is from 5.5 to 9.0 equal to 4.5 ev.

Then, we need to find the speed of the electron to gain a kinetic energy of 4.5 ev from the equation KE = (1/2) m*v^2

Where,

KE = 4.5 ev * 1 J / (6.242*10^18) ev = 7.2098 * 10^ - 19 J

m = mass of the electron = 9.11 * 10 ^ - 31 kg

v = √ (2 * KE/m) = √[ 2*7.2098 * 10 ^ - 19 kg / (9.11*10^-31kg) = 1,258,107 m/s

Answer: 1,258,107 m/s