Answer
Since the kinetic energy of the electron is $4.81~eV$, which is greater than $4.00~eV$, the electron is able to excite the atom from the $n=1$ state to the $n = 2$ state.
Since the kinetic energy of the electron is $4.81~eV$, which is less than $6.00~eV$, the electron is not able to excite the atom from the $n=1$ state to the $n = 3$ state.
Work Step by Step
We can find the kinetic energy of the electron:
$K = \frac{1}{2}mv^2$
$K = (\frac{1}{2})(9.109\times 10^{-31}~J)(1.30\times 10^6~m/s)^2$
$K = 7.697\times 10^{-19}~J$
$K = (7.697\times 10^{-19}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$K = 4.81~eV$
The energy difference between the $n = 1$ state and the $n = 2$ state is $4.00~eV$
Since the kinetic energy of the electron is $4.81~eV$, which is greater than $4.00~eV$, the electron is able to excite the atom from the $n=1$ state to the $n = 2$ state.
The energy difference between the $n = 1$ state and the $n = 3$ state is $6.00~eV$
Since the kinetic energy of the electron is $4.81~eV$, which is less than $6.00~eV$, the electron is not able to excite the atom from the $n=1$ state to the $n = 3$ state.
