Answer
(a) Since the kinetic energy of the electron is $2.00~eV$, which is greater than $1.50~eV$, the electron is able to excite the atom from the $n=1$ state to the $n = 2$ state.
(b) The electron's kinetic energy after the collision is $~~0.50~eV$
Work Step by Step
(a) $E_3 = 4.00~eV$
$E_2 = 1.50~eV$
$E_1 = 0~eV$
The energy difference between the $n=1$ state and the $n = 2$ state is $1.50~eV$
Since the kinetic energy of the electron is $2.00~eV$, which is greater than $1.50~eV$, the electron is able to excite the atom from the $n=1$ state to the $n = 2$ state.
(b) The atom will absorb $1.50~eV$ of energy from the electron.
The electron's kinetic energy after the collision is $~~2.00~eV - 1.50~eV~~$ which is $~~0.50~eV$