We analyze the quantum properties of the light generated by a two-level laser with an open cavity and coupled to a vacuum reservoir via a single-port mirror. The two-level laser consists of two-level atoms available in an open cavity and pumped from the lower to the upper level by means of electron bombardment. We seek to carry out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the large-time approximation scheme, we have obtained the steady-state solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators. Using the resulting steady-state solutions, we have calculated the mean photon number, the variance of the photon number, and the quadrature variance for cavity light. It is found that the two-level laser generates coherent light for $\gamma + \gamma_c \ll r_a$ and chaotic light for $\gamma + \gamma_c = r_a$. Moreover, we have established that a large part of the total mean photon number is confined in a relatively small frequency interval. We have also established that the mean photon number in the presence of spontaneous emission is less than that in the absence of spontaneous emission. In other words, the effect of spontaneous emission is to decrease the mean photon number.