## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The electron is able to excite the atom from the $n=1$ state to the $n = 2$ state. The electron is not able to excite the atom from the $n=1$ state to the $n = 3$ state.
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.