We give a simple semiclassical derivation of the radiative mean lifetime \ensuremath{\tau}(${\mathit{n}}_{\mathit{r}}$) of an electron in a bound state in a uniform magnetic field B, that is, in a Landau state. The state is characterized by two quantum numbers ${\mathit{n}}_{\mathit{r}}$ and ${\mathit{n}}_{\mathit{l}}$ and by the velocity component ${\mathit{v}}_{\mathit{z}}$ of the electron parallel to B, but \ensuremath{\tau} is independent of ${\mathit{n}}_{\mathit{l}}$ and ${\mathit{v}}_{\mathit{z}}$; ${\mathit{n}}_{\mathit{r}}$ and ${\mathit{n}}_{\mathit{l}}$ are the right and left circular Landau quantum numbers. The approach used is similar to that which has been applied in the semiclassical estimation of the radiative mean lifetime \ensuremath{\tau}(n,l) of an electron in a hydrogenlike state with quantum numbers n and l. As in that case, the results become exact only in the limit in which the relevant quantum number(s)---in the present case ${\mathit{n}}_{\mathit{r}}$---approach infinity, but \ensuremath{\tau}(${\mathit{n}}_{\mathit{r}}$) is reasonably accurate even for ${\mathit{n}}_{\mathit{r}}$ rather small. ${\mathit{L}}_{\mathit{z}}$, the z component of the orbital angular momentum of an electron in the field B=Be${\mathrm{^}}_{\mathit{z}}$, need not normally be considered, since the equation of motion is known. (The equation is gauge independent and only the rate of change of ${\mathit{L}}_{\mathit{z}}$ is necessary to estimate the mean lifetime.) However, since the change in ${\mathit{L}}_{\mathit{z}}$ accounts for the angular momentum given up to the photon which is radiated and since ${\mathit{L}}_{\mathit{z}}$ is formally gauge dependent, it is worth studying by itself. We evaluate ${\mathit{L}}_{\mathit{z}}$ in several ways; in one evaluation, the field B=Be${\mathrm{^}}_{\mathit{z}}$ is simulated by a magnetic monopole placed at a great distance from the circulating electron. We find that ${\mathit{L}}_{\mathit{z}}$ is half the mechanical orbital angular momentum and therefore that the field contribution to the total angular momentum cannot be omitted when applying angular momentum conservation.