We report calculations of the ground state transition energies and the radiative lifetimes in InxGa1-xN/AlN quantum dots with different size and indium content. The ground state transition energy and the radiative lifetime of the InxGa1-xN/AlN quantum dots can be varied over a wide range by changing the height of the quantum dot and the indium content. The sizes and compositions for quantum dots emitting in the wavelength range for fiber-optic telecommunications have been found. The radiative lifetime of the InxGa1-xN/AlN quantum dots increases with increase in quantum dot height at a constant indium content, and increases with increase in indium content at constant quantum dot height. For quantum dots with constant ground state transition energy the radiative lifetime decreases with increase in indium content.